option bounds with finite revision opportunities this article generalizes the single period linear programming bounds on option prices by allowing for a finite number of revision opportunities it is shown that in an incomplete market the bounds on option prices can be derived using a modified binomial option pricing model tighter bounds are developed under more restrictive assumptions on probabilities and risk aversion for this case the upper bounds are shown to coincide with the upper bounds derived by perrakis while the lower bounds are shown to be tighter in 1984 perrakis and ryan 6 derived upper and lower bounds on european option prices in discrete time and under modest assumptions on preferences and

subjective stochastic dominance put writing and stock purchases with extensions to option pricing and portfolio composition initially an investor has the choice of two risky assets writing a european put option or buying the underlying share under broad conditions a risk averse investor will be subjectively better off writing the put when homogeneous expectations are invoked an upper bound for the put premium is obtained a numerical example using the lognormal density function illustrates the broad conditions for risk averters subjectively preferring the put writing strategy additional conditions permit this preference for writing puts to be extended to the portfolio context transactions costs only reinforce this preference in the one period horizon considered

upper and lower bounds of put and call option value stochastic dominance approach applying stochastic dominance rules with borrowing and lending at the risk free interest rate we derive upper and lower values for an option price for all unconstrained utility functions and alternatively for concave utility functions the derivation of these bounds is quite general and fits any kind of stock price distribution as long as it is characterized by a nonnegative beta transaction costs and taxes can be easily incorporated in the model presented here since investors are not required to revise their portfolios continuously the price that is paid for this generalization is that a range of values rather than a unique value is obtained in the last decade there has been an increasing interest in the options market by both academicians and practitioners the most well known valuation models are the black scholes 4 model the jump stochastic process model see cox and ross 6 the binomial model see cox ross and rubinstein 7 rendleman and bartler 19 and sharpe 22 and rubinstein s discrete model 21 recently perrakis and ryan 18 using rubinstein s approach have derived upper and lower bounds for option prices the relative pricing theory of contingent claims differs in the continuous time and discrete time models in a continuous time framework the instantaneous expected rate of return of the option and that of the underlying stock must follow a certain market equilibrium condition in this case the equilibrium condition is easily determined by a continuous hedging strategy in the discrete time case there is no hedging strategy to provide a simple relationship between the option and the stock price however for a given value distribution of the stock the value distribution of the option is uniquely determined by the option exercise price and this suggests some possible relationships between the stock and option values

comparing risks by acceptance and rejection stochastic dominance is a partial order on risky assets gambles that is based on the uniform preference of all decision makers in an appropriate class for one gamble over another we modify this requirement first by taking into account the status quo given by the current wealth and the possibility of rejecting gambles and second by comparing rejections that are substantive i e uniform over wealth levels or over utilities this yields two new stochastic orders wealth uniform dominance and utility uniform dominance unlike stochastic dominance these two orders are complete any two gambles can be compared moreover they are equivalent to the orders induced by respectively the aumann serrano index of riskiness and the foster hart measure of riskiness

multi objective stochastic programming for portfolio selection abstract generally in the portfolio selection problem the decision maker dm considers simultaneously conflicting objectives such as rate of return liquidity and risk multi objective programming techniques such as goal programming gp and compromise programming cp are used to choose the portfolio best satisfying the dm s aspirations and preferences in this article we assume that the parameters associated with the objectives are random and normally distributed we propose a chance constrained compromise programming model cccp as a deterministic transformation to multi objective stochastic programming portfolio model cccp is based on cp and chance constrained programming ccp models the proposed program is illustrated by means of a portfolio selection problem from the tunisian stock exchange market

stochastic dominance decision rules when the attributes are utility independent in multivariate decisions under risk assessing the complete utility function can be a major obstacle decision rules are investigated which characterize uniformly better alternatives with respect to a whole class of utility functions in this paper independence assumptions are imposed on the preference structure while the levels of attributes may be stochastically dependent in an arbitrary way the utilities considered are additive multiplicative or multilinear necessary and sufficient conditions are developed for uniform decisions over utilities with common substitutional structure and where the univariate conditional utilities show qualitative properties such as risk aversion the rules are direct extensions of known univariate rules and easy to evaluate

omega performance measure and portfolio insurance abstract we analyze the performance of the two main portfolio insurance methods the obpi and cppi strategies using downside risk measures for this purpose we introduce kappa performance measures and especially the omega measure these measures take account of the entire return distribution we show that the cppi method performs better than the obpi as a by product we determine the set of threshold values for these risk reward performance measures

on option pricing bounds the purpose of this article is to compare the perrakis and ryan bounds of option prices in a single period model with option bounds derived using linear programming it is shown that the upper bounds are identical but that the lower bounds are different a comparison of these bounds together with merton s bounds and the black scholes prices in a lognormal securities market is presented the black scholes 1 option pricing model is preference free its simplicity derives from the continuous trading assumption which enables a portfolio of stock and bonds to be constructed so as to replicate the payouts of the option in an incomplete market with only finite opportunities to revise portfolios no preference free option price can be constructed 3 6 for this case preferencedependent prices can be established rather than place restrictive assumptions on preferences perrakis and ryan pr 5 have recently derived upper and lower bounds for a single and multiple period call option price the development of these bounds is based on the single price law and arbitrage arguments and requires modest assumptions on preferences the bounds exist as equilibrium values given a consensus on stock price distributions in this article we shall develop bounds for option prices based on primitive prices in incomplete markets and compare these bounds to the single period bounds derived by perrakis and ryan towards this goal we first review the pricing approach for primitive securities and proceed to re express the pr bounds as derived from their arbitrage portfolios then using linear programming bounds on option prices are derived linear programming approaches for obtaining relationships among option prices have been investigated garman 2 for example established an algebra for evaluating hedge portfolios using this algebra a one period linear program can be established that provides a way to search for arbitrage opportunities over an infinite number of portfolio strategies one of the features of the algebra is that only one linear program need be solved to determine if riskless arbitrage strategies can be established by investigating the dual of the linear program garman obtained necessary and sufficient conditions for rational option pricing in a one period setting these bounds were shown to be consistent with the bounds determined by merton 4 unlike garman s approach the linear programming approach presented here places constraints on time preferences risk aversion and state probabilities under specific sets of assumptions linear programs are formulated where the objective function to be optimized is the call price minimization and maximi

growth and the effects of inflation abstract in this paper we study the relationship between the rate of increase of the money supply and the rate of growth of output in an economy we show that in some models of endogenous growth inflation has direct effects on the growth rate of the economy despite this the estimated welfare cost of inflation from calibrated examples is similar to that found in exogenous growth models

the rationale of the mean standard deviation analysis skewness preference and the demand for money publisher summary this chapter discusses the rationale of the mean standard deviation analysis skewness preference and the demand for money in january 1969 issue of the review of economic studies karl borch and martin feldstein separately criticized the widely used mean variance analysis of portfolio selection borch contended that any system of upward sloping mean standard deviation e s indifference curves can be shown to be inconsistent with the basic axiom of choice under uncertainty he pointed out that one can always pick any two points on an upward sloping indifference curve to represent two bernoulli distributions with probability 1 p of gaining the same amount x in both the cases and probability p of gaining y1 in the case of one distribution and y2 in the case of the second distribution with y2 y1 if the second distribution represents the point to the northeast of the other point then by the dominance axiom the second distribution must be preferred to the first which contradicts the basic meaning of indifference curves feldstein by using a log utility function and a lognormal distribution for investment outcome showed that e s indifference curves for a risk averter need not be convex downwards though upward sloping they would change from convex to concave once the standard deviation of the outcome exceeds the mean multiplied by on the face of it this seems to suggest that risk aversion might decrease as risk is increased beyond a certain extent

money and growth an alternative approach this paper takes an alternative approach to the topic of money and growth by developing a model in which the effects of sustained capital accumulation on an evolving system of payments in addition to the conventional effects of sustained inflation on growth are examined while the effects of inflation on growth are small the effects of growth on the monetary system are substantial the results are consistent with ideas about money and growth contained in work that predates that of james tobin and miguel sidrauski as well as with evidence that money and asset demands vary systematically within economies as they develop copyright 1994 by american economic association

almost stochastic dominance and stocks for the long run abstract the geometric mean argument and the recently developed almost stochastic dominance criterion have been employed to make the case for stocks for the long run we show that almost stochastic dominance and the geometric mean argument do not necessarily support long run investment in equities in fact for standard preferences bonds may be preferred to stocks for the long run while stocks are preferred for shorter horizons

ranking occupations as risky income prospects this study investigates the problem of how best to measure the income attractiveness of various occupations allowing for the differences among occupations in their stability of income analyzing data for eleven occupations from the one percent public use sample of the 1970 u s census of occupations the authors demonstrate the weaknesses of measures used in previous studies and the advantages of using stochastic dominance analysis

risk efficient irrigation strategies for wheat abstract agricultural production is risky when farmers are risk averse they are likely to put a premium on production methods that reduce perceived risks irrigation is generally believed to be a risk reducing input by using the concept of stochastic dominance risk efficient irrigation policies for wheat grown in central india are identified and quantitative estimates of benefits due to risk reduction are obtained such benefits were found to be of a large order of magnitude the more common methods such as mean variance analysis tended to over estimate the benefits

day of the week effect in the taiwan foreign exchange market abstract this study uses stochastic dominance with and without risk free assets to examine whether trading days can affect patterns of the day of the week effect in the taiwan foreign exchange market our results generally indicate that higher returns appear on the first three days of the week across different trading day regimes in the taiwan foreign exchange market confirming day of the week effect allocating part of investors assets in risk free assets is useful in distinguishing returns among weekdays for all currencies

the effects of shifts in a return distribution on optimal portfolios when the distribution of the returns of a risky asset undergoes a stochastically dominating shift a risk averse investor may not necessarily increase the investment in that asset this paper provides restrictions on the investor s utility function that are necessary and sufficient for a dominating shift to bring about no decrease in the investment in the respective asset if there are two risky assets in the portfolio these conditions are also necessary if there are n 2 assets and are necessary and sufficient if the utility function exhibits constant absolute risk aversion copyright 1990 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

on the role of information in decision making the case of sorghum yield in burkina faso this paper investigates the role of temporal uncertainty and information issues in economic decisions it shows that the nature of the economic environment e g the production technology can influence the valuation of information which in turn affects the choice functions this is illustrated by an empirical application to sorghum yield response analysis in burkina faso the paper stresses the importance of technology and information valuation in risk behaviour

a stochastic dominance comparison of water conserving irrigation strategies stochastic dominance and stochastic dominance with respect to a function are used to compare water conserving irrigation strategies in an area of declining ground water supplies a computerized grain sorghum plant growth model using daily weather observations provides the basis for stochastic dominance comparisons six irrigation strategies dominate contemporary intensive irrigation practices by first degree stochastic dominance and two additional strategies exhibit second degree stochastic dominance over contemporary practices dominant strategies involve irrigating based on a 45 percent soil water criterion and eliminating early season irrigations some dominant strategies reduce water use by as much as 40 percent while increasing expected net returns

the use of risk and return models for multiattribute decisions with decomposable utilities normatively oriented approaches to decision making under uncertainty occupy a major portion of the literature of decision analysis among the proposed approaches the von neumann morgenstern expected utility eu theory has been the most prominent model of rational choice despite some controversies that surround this model with respect to its descriptive ability as well as the plausibility of utility assessment in actual decision situations 6 10 although most applications of the eu model have been concerned with decisions involving monetary outcomes its scope is not limited to any particular class of conse quences the basic appeal of the model is attributable partly to its generality in this regard and more importantly to the apparent reasonableness of its preferentialaxioms in the context of decisions with monetary outcomes several alternatives to the eu model have been proposed including the mean variance and mean semivariance models that have found popularity in the economies and finance litera ture see 4 8 and 9 in contrast to the eu theory where a decision maker s preferences among uncertain prospects are assumed given preferences in these models are formulated in terms of two attributes that are presumed to character ize all available choices in the mean semivariance model for example uncer tain prospects are viewed entirely in terms of their means and below target semivariances a generalization of this model was examined by fishburn 2 who showed that the general mean risk model exhibits a certain degree of compatibility with the eu model more recently holthausen 5 showed that this compatibility is significantly enhanced when mean is replaced by a return measure de fined as a probability weighted function of above target deviations specifically holthausen proved that this model yields the same preferences as the eu model whenever the expected utility function has the form

an empirical comparison of stochastic dominance among lognormal prospects l introduct ion the theory of portfolio selection and diversification developed by markowitz 22 and tobin 33 was based primarily on the criterion of meanvariance mv efficiency the objective was to select an efficient set of portfolios from which every risk averter will choose the optimal portfolio which maximizes his expected utility the mv criterion is the appropriate rule either for the case in which the utility function is quadratic or if the returns are normally distributed and risk aversion is assumed two approaches to the choice among risky alternatives that have been developed independently over the past two decades are the geometric mean criterion gm and the stochastic dominance sd decision model both can be justified by the expected utility hypothesis with the geometric mean cri terion following as a result of the assumption that the decision maker has a logarithmic utility function and the stochastic dominance models requiring the less restrictive assumption of signs of the first few derivatives of the decision maker s utility function this paper compares the concept of ordinary stochastic dominance to stochastic dominance of the lognormally distributed prospects from an empirical point of view further 1ight is also shed on the issue of applying the markowitz tobin mean variance rule

an empirical analysis of term premiums using stochastic dominance abstract this paper examines term premiums in u s treasury bill monthly holding period returns several techniques are employed to ascertain whether the observed term premiums are economically meaningful no second order stochastic dominance is found in the first five month maturities when a riskless asset is assumed the first two maturities are dominated therefore we conclude that although there are statistically significant term premiums they are not economically meaningful if there is no riskless borrowing and lending the term premiums are economically meaningful in the sense that the longer maturities dominate the shorter maturities when a riskless asset is available

large and small baseload power plants drivers to define the optimal portfolios despite the growing interest in small medium sized power plants smpp international literature provides only studies related to portfolios of large plants in infinite markets grids with no particular attention given to base load smpp this paper aims to fill this gap investigating the attractiveness of smpp portfolios respect to large power plant portfolios the analysis includes nuclear coal and combined cycle gas turbines ccgt of different plant sizes the mean variance portfolio theory mvp is used to define the best portfolio according to internal rate of return irr and levelised unit electricity cost luec considering the life cycle costs of each power plant carbon tax electricity price and grid dimension the results show how large plants are the best option for large grids while smpp are as competitive as large plants in small grids in fact in order to achieve the highest profitability with the lowest risk it is necessary to build several types of different plants and in case of small grids this is possible only with smpp a further result is the application of the framework to european oecd countries and the united states assessing their portfolios

stochastic dominance vs mean variance portfolio analysis an empirical evaluation most of the work in portfolio theory in the past decade has been based on the principle of utility maximization where either the investor s utility function is assumed to be a second degree polynomial with a positive first derivative and a negative second derivative or the probability functions are assumed to be normal if at least one of these conditions holds it can be shown that choosing among risky assets on the basis of their mean and variance only is consistent with the von neumann morgenstern utility maximization model thus given the above assumptions the incorporation of higher moments of a distribution and the adoption of alternative approaches to portfolio selection have largely been ignored in favor of the more familiar mean variance approaches

stochastic dominance in an ordinal world abstract existing stochastic dominance rules apply to variables such as income wealth and rates of return all of which are measured on cardinal scales this study develops and applies stochastic dominance rules for ordinal data it is shown that the new rules are consistent with the traditional von neumann morgenstern expected utility approach and that they are applicable and relevant in a wide variety of managerial decision making situations where existing stochastic dominance rules fail to apply we apply ordinal sd rules to the transformation of random variables

market reaction to quarterly earnings announcements a stochastic dominance based test of market efficiency the use of the capm in empirical research is subject to some criticism in light of this criticism the stochastic dominance criteria are offered as an alternative research method for the examination of market efficiency the underlying assumptions of the two frameworks are discussed and the stochastic dominance technique is demonstrated via the examination of market reaction to quarterly earnings announcements during the 24 quarters commencing with october 1962 the findings are compared to those of watts watts r the time series behavior of quarterly earnings unpublished paper university of newcastle newcastle n s w 1975 quoted in watts 1978 who utilized the same data base in contrast to watts conclusion our analysis suggests that the market was efficient during the entire period examined and that no significant differences in market behavior between the first and the second 12 month periods was evident the discord may be attributed to the relative effectiveness of the two analytical tool

agricultural trade negotiations as a strategic game abstract this study views multilateral trade negotiations as a strategic game among nations or regions including taxpayer consumer and producer components payoffs are calculated from an intermediate run international trade model initialized with 1989 data for the public at large the nash equilibrium and socially optimal outcome is liberalization of trade unilateral or multilateral maintenance of the status quo of market distortions costing the world billions of dollars each year is rational only if producer payoffs are sovereign so that strategies optimal for producers are considered optimal for nations remedial policies are discussed including opportunities for economic education political system reform and less incentives for producers to scuttle multilateral trade negotiations

trade wars trade negotiations and applied game theory what is the value of trade negotiations quantitative measures of the value of trade liberalisation generally ignore the strategic aspects of protection policy the traditional approach is to compare welfare levels under the existing structure of protection with welfare levels under some alternative structure of protection such as unilateral or multilateral free trade we add two additional questions first in a non cooperative context are either of these points of comparison consistent with countries adopting best response policies given the policies of other countries second in the context of a cooperative negotiation are either of these points of comparison consistent with the outcome that meets certain plausible criteria for a bargaining process if the answer to either of these questions is no then the traditional approach provides at best an incomplete answer to the original question and could provide a misleading answer a simple example illustrates our basic point consider the game in table i this is a non cooperative game between the united states and ec in which each agent has just two pure strategies to do nothing and keep k the existing structure of protection in place or to abolish a trade barriers on imports from the other agent only the payoffs shown are the annual welfare impact relative to the status quo as measured by the equivalent variation ev in income in billions of i973 u s dollars the values shown are taken from the simulation results of brown and whalley i980 table i 4 p 864 what is the best response of the united states in this context if the ec decides to keep its protection structure the united states does better by also keeping its protection structure intact in other words given that the ec plays k it is a best response for the united states to also play k thus the traditional approach would imply that the united states gains from protection in this case however what is the best response of the united states if the ec decides to abolish its protection structure in this instance the united states does best by also abolishing its protection structure the point here is simply that the welfare cost of protection to the united states depends on what the ec does without saying something about what the ec will do one cannot answer our question vis a vis the united states as it happens in this particular game we

conservation payments under risk a stochastic dominance approach conservation payments can be used to preserve forest and agroforest systems to explain landowners land use decisions and determine appropriate conservation payments it is necessary to focus on revenue risk marginal conditional stochastic dominance rules are used to derive conditions for determining the conservation payments required to guarantee that the environmentally preferred land use dominates an empirical application to shaded coffee protection in the biologically important choco region of west ecuador shows that conservation payments required for preserving shaded coffee areas are much higher than those calculated under risk neutral assumptions further the extant distribution of land has strong impacts on the required payments

foundations of decision analysis along the way this paper offers a personal perspective on the development of decision theory and related subjects during the past half century it first reviews six milestones in the foundations of decision analysis that are associated with frank p ramsey john von neumann and oskar morgenstern leonard j savage maurice allais and ward edwards west churchman and russell ackoff and kenneth arrow it then gives a personal account of further developments over the past 30 years in linear utility theory subjective probability and ambiguity nonlinear preference and utility stochastic dominance and inequality analysis multiattribute utility theory and the theory of social choice the paper could be viewed as a supplement to my extensive review of utility theory in management science some 20 years ago however it makes no claim of completeness since its main aim is to recall important debts and describe what it has been like to be a part of the development of decision analysis in the past few decades

option bounds in discrete time extensions and the pricing of the american put in a recent paper perrakis and ryan 1984 upper and lower bounds on european option prices were derived in discrete time these bounds were based on an extension of the discrete time derivation of black scholes pricing first presented in the work of black and scholes 1973 the bounds are functions of the stock and exercise prices the riskless rate of interest the time to maturity and the entire distribution of stock returns in other words they need more information than black scholes for their computation and the derived results are weaker on the other hand they are significantly more general in their assumptions insofar as they do not rely on the continuous time riskless hedge of the original black scholes derivations or on the assumption of a binomial distribution of stock returns used in cox ross and rubinstein 1979 and rendleman and bartter 1979 for this reason they are likely to be particularly useful in valuing options on assets for which the black scholes methodology is clearly this paper generalizes and tightens the discrete time bounds for european options and develops similar bounds for american puts the stock return has a distribution with a finite range and is subject to the restriction that the stock be nonnegative beta the bounds are derived from arbitrage portfolios using the stock the option and the riskless asset they converge to the previous ones when the range coincides with the nonnegative real line and they both become equal to the binomial option model under a two state stock return upper and lower bounds for the american put are derived recursively by the same method with arbitrage portfolios involving the stock the riskless asset and american and european puts an example is provided with a trinomial return distribution part of this research was done while i was a visiting professor 1983 84 ecole superieure de commerce et d administration des entreprises reims france i wish to thank peter ryan albert madansky and a referee of this journal for helpful advice and comment while retaining all responsibility for any remaining errors or omissions 1 note however that this is also true of other blackscholes generalizations such as merton 1976

ordering uncertain options under inflation a note stochastic dominance rules sd have been extended to the case where investors are allowed to borrow and lend at the riskless interest rate stochastic dominance rules with a riskless asset sdr are much more effective than sd rules however it seems that this benefit is eliminated by an uncertain inflation since riskless assets become risky once uncertain inflation is considered we prove in this paper that sdr criteria are valid also in the face of uncertain and independent inflation moreover while the mean variance mv efficient set increases with uncertain inflation the stochastic dominance efficient sets decrease stochastic dominance criteria sd for ordering risky assets were developed mainly in the late sixties following the development of the mean variance rule mv and the capital asset pricing model capm by analogy to the extension of sharpe and lintner of the mv criterion levy and kroll 10 have extended the sd rules by allowing borrowing and lending at the riskless interest rate this extension sharply decreases the size of the efficient set and in some cases an empirical separation is obtained or almost a separation where the efficient set of risky assets includes only one or two risky portfolios see levy and kroll 11 note however that these important economic results rely on the assumption that a riskless asset indeed exists an assumption which cannot be defended in a period of uncertain inflation chen and boness 2 roll 17 and friend et al 5 investigate the impact of inflation on the capm chen and boness assume a quadratic utility function and also make the assumption that the real rate of return is given by the nominal rate of return less the inflation hence ignoring the cross product of inflation and rates of return which greatly simplifies the mathematical analysis roll also assumes a quadratic utility function and further makes the assumption that a riskless asset in real terms exists friend et al assume that returns are generated by a wiener process the investment horizon is infinitesimal and that investors are characterized by constant proportional risk aversion under these assumptions they derive a formula which is analogous to the capm where inflation a random variable is incorporated in the formula it should be noted that by an infinitesimal investment horizon they do away with the cross product of inflation and the rates of return which is equal to zero in this specific case the relationship between the inflation rate and stock prices has been a subject

two moment decision models and expected utility maximization two moment decision models are consistent with expected utility maximization only if the choice set or the agent s preferences are restricted this paper identifies a restriction which is sufficient to ensure this consistency and confirms that it holds in many economic models the implications for economic analysis are then derived two different approaches to representing an agent s preferences over strategies yielding random payoffs are in wide use under the mean standard deviation ms approach the agent is assumed to rank the alternatives according to the value of some function defined over the first two moments of the random payoff while the expected utility eu criterion assumes that the expected value of some utility function defined over payoffs is used instead the fact that there are these two competing approaches has generated a considerable literature some authors are concerned with the advantages and disadvantages of each while others deal with conditions under which the potentially different approaches would yield the same results or at least approximately so space does not

econometric estimation of producers risk attitudes general methods are proposed for the identification and econometric estimation of the parameters of the distribution of risk attitudes in a producer population the proposed methods also provide the basis for the development of statistical tests of model specification and of behavioral hypotheses econometric risk attitude estimation is shown to be possible under less restrictive conditions than previously believed a moment based version of the general model is applied to indian data and the econometrically estimated risk attitudes are presented and compared to experimental results for a similar group of producers

empirical tests for stochastic dominance efficiency we derive empirical tests for the stochastic dominance efficiency of a given portfolio with respect to all possible portfolios constructed from a set of assets the tests can be computed using straightforward linear programming bootstrapping techniques and asymptotic distribution theory can approximate the sampling properties of the test results and allow for statistical inference our results could provide a stimulus to the further proliferation of stochastic dominance for the problem of portfolio selection and evaluation using our tests the fama and french market portfolio is significantly inefficient relative to benchmark portfolios formed on market capitalization and book to market equity ratio

optimal fiscal and monetary policy in an economy without capital abstract this paper is concerned with the structure and time consistency of optimal fiscal and monetary policy in an economy without capital in a dynamic context optimal taxation means distributing tax distortions over time in a welfare maximizing way for a barter economy our main finding is that with debt commitments of sufficiently rich maturity structure an optimal policy if one exists is time consistent in a monetary economy the idea of optimal taxation must be broadened to include an inflation tax and we find that time consistency does not carry over an optimal inflation tax requires commitment by rules in a sense that has no counterpart in the dynamic theory of ordinary excise taxes the reason time consistency fails in a monetary economy is that nominal assets should from a welfare maximizing point of view always be taxed away via an immediate inflation in a kind of capital levy this emerges as a new possibility when money is introduced into an economy without capital

data envelopment analysis of mutual funds based on second order stochastic dominance abstract although data envelopment analysis dea has been extensively used to assess the performance of mutual funds mf most of the approaches overestimate the risk associated to the endogenous benchmark portfolio this is because in the conventional dea technology the risk of the target portfolio is computed as a linear combination of the risk of the assessed mf this neglects the important effects of portfolio diversification other approaches based on mean variance or mean variance skewness are non linear we propose to combine dea with stochastic dominance criteria thus in this paper six distinct dea like linear programming lp models are proposed for computing relative efficiency scores consistent in the sense of necessity with second order stochastic dominance ssd the aim is that being ssd efficient the obtained target portfolio should be an optimal benchmark for any rational risk averse investor the proposed models are compared with several related approaches from the literature

an empirical analysis of term premiums using significance tests for stochastic dominance abstract the economic significance of term premiums in real returns on us treasury bills is examined using recently developed tests for first and second order stochastic dominance the tests place only general restrictions on the preferences of individuals and on the distribution of returns the results indicate that the two month real return is preferred to the one month real return based on both dominance criteria other term premiums do not appear to be economically significant

money and asset prices in a cash in advance economy an asset pricing model with money introduced via a cash in advance constraint is presented the monetary velocity is variable hence money demand does not obey the trivial quantity equation the effects of disturbances in output and money growth on real balances the price level and interest rates are examined monetary policy has effects on real asset prices the fisher relation and the premium on nominal bonds are discussed the precise role of the timing of information and transactions for properties of price levels and interest rates are clarified

distributional analysis of portfolio choice trading in a market is compared with receiving some particular consu mption bundle given increasing state independent preferences and complete markets the analysis focuses on the distribution price of t he particular bundle the distributional price is the price of the ch eapest utility equivalent bundle sold in the market the distribution al price is determined by the distribution functions of the outside b undle and the state price density simple portfolio performance measu res illustrate the value of the approach unlike capm based measures these measures are valid even when superior information is the sourc e of superior performance copyright 1988 by the university of chicago

mean gini portfolio theory and the pricing of risky assets this paper presents the mean gini mg approach to analyze risky prospects and construct optimum portfolios the proposed method has the simplicity of a mean variance model and the main features of stochastic dominance efficiency since mean gini is consistent with investor behavior under uncertainty for a wide class of probability distributions gini s mean difference is shown to be more adequate than the variance for evaluating the variability of a prospect the mg approach is then applied to capital markets and the security valuation theorem is derived as a general relationship between average return and risk this is further extended to include a degree of risk aversion that can be estimated from capital market data the analysis is concluded with the concentration ratio to allow for the classification of different securities with respect to their relative riskiness

geometric mean approximations in 1959 henry latana 2 proposed an approximation to the geometric mean that was a simple function of the arithmetic mean and variance thereby indicating a mathematical relationship between the risky investment choice model of bernoulli and the markowitz mean variance model in 1969 young and trent 4 presented empirical test results of the latane approximation as well as a set of other approximations to the geometric mean based on moments and concluded that the latane formula yielded a quite accurate approximation to the geometric mean in jean s 1980 paper 1 relating the geometric mean model to stochastic dominance models the infinite series representation of the geometric mean used suggests a more accurate approximation with moments of the geometric mean than that contained in the earlier papers may be possible various forms of that series expressed in alternate origin moments are tested empirically below and the results confirm that this later series does yield the greatest accuracy of the three approaches

multivariate decision making abstract consider a set of multivariate risky options a partial ordering of these options is quite difficult and even for the two dimensional case a knowledge of the cross derivatives of the decision maker s utility function is required in this paper we establish first degree multivariate stochastic dominance by applying the concepts of the indirect utility function and the indirect probability distribution thus we reduce the complex multivariate risky option into a univariate risky option where the random variable is the derived indirect income the second degree stochastic dominance rule is also derived under certain restrictions on the utility function

agency theory and stochastic dominance recently agency theory has become popular as a means of explaining the structure of contracts between various classes of economic agents oftentimes the contracts of interest represent sharing rules for the payoffs that result from some production activity in the usual two party model of the contracting problem one party designated the principal delegates authority for decisions affecting production to another party designated the agent typically the assumptions made about the consequences of the agent s actions are that they are associated with effort on the part of the agent for which the agent but not the principal has disutility and that greater effort will result in higher payoffs from production in every state of nature moral hazard is then introduced by assuming that the principal is unable to observe the agent s effort or to infer what effort the agent applied through an ex post observation of the payoff that results

impact of the 1996 us fair act on the common agricultural policy in the world trade organisation context the decoupling issue abstract the united states us federal agriculture improvement and reform fair act of 1996 represents a watershed not only from a domestic point of view but also from the perspective of the next round of international agricultural negotiations in particular it will force the european union eu to reform its agricultural policy so that compensatory payments for support price cuts are included in the green box or at least are much more decoupled than at present us exports of several agricultural products including maize pork and poultry meat barring a prolonged global economic downturn should increase substantially over the 7 year period of the act and beyond accordingly the us will certainly attempt to ensure that trade barriers with the eu and subsidised competition from the eu in third markets are kept to a minimum though the 1999 eu proposals for a new reform of the common agricultural policy cap represent a courageous step in the right direction they are likely to be insufficient to comply with future world trade organisation wto commitments in particular with regard to the decoupling of direct aid payments we have made a number of proposals for an internal support policy which explicitly recognises that european farmers have several functions that require specific forms of public intervention and which should comply with future wto requirements

option pricing bounds in discrete time upper and lower bounds are derived for call options traded at discrete intervals these bounds are independent of assumptions on the stock price distribution other than a restriction satisfied by the stock being non negative beta the development of the bounds relies on the single price law and arbitrage arguments both single period and multiperiod results are produced and put option bounds follow by extension the bounds exist as equilibrium values given a consensus on stock price distribution they are also valid for empirical studies being adjustable for dividends and commissions following the impetus of the black scholes pricing model the majority of option analyses have been in continuous time such approaches have relied on the formation of perfect riskless hedges involving the option its underlying security and a riskless asset since the hedge must be continuously revised and maintained while actual trading opportunities are discrete this crucial assumption limits the accuracy and applicability of the black scholes and related formulae in fact the black scholes formula can only be considered as a valid approximation to the discrete time solution merton 8 p 663 while the closeness of that approximation has not been ascertained in general 1 earlier discrete models such as boness 3 and samuelson 12 have been succeeded by those of brennan 5 cox et al 6 and rubinstein 11 in which distributional restrictions are imposed on share returns usually the discrete formula converges to the black scholes expression under appropriate limit conditions using the rubinstein 11 approach we derive upper and lower bounds for option prices with both a general price distribution and discrete trading opportunities the bounds are functions of the share and exercise prices the riskless rate of interest the distribution of the share price change per period and the number of periods of expiration of the option the lower bound is tighter than that of merton 7 derived from more general arbitrage considerations while being less exact than the results already mentioned for restricted distributions

the relationship between arbitrage and first order stochastic dominance this paper joins together two fields of research in financial economics the first field studies stochastic dominance while the second field studies arbitrage pricing the two fields are linked together through the derivation and the proof of a characterization theorem the characterization theorem gives necessary and sufficient conditions for the existence of arbitrage opportunities in terms of the existence of two assets one of which first order stochastically dominates the other and the price of a particular contingent claim examples are provided to demonstrate the theorem s content this paper joins together two fields of research in financial economics the first field studies portfolio choice from the perspective of stochastic dominance see hadar and russell 5 6 hanoch and levy 7 levy and kroll 13 the second field studies arbitrage pricing its characterization and implications see ross 15 kreps 12 harrison and kreps 8 harrison and pliska 9 in these fields it is well known that the existence of arbitrage opportunities implies first order stochastic dominance and that the converse does not hold this paper provides a set of conditions under which the converse is true given complete markets the existence of an arbitrage opportunity is characterized in terms of the existence of two traded assets one of which stochastically dominates the other along with one additional condition the additional condition is roughly that state contingent prices must be zero over the states where the first asset dominates the second the theorem has a qualification however it is applicable only in markets which are complete not in the arrow debreu sense but in a weaker sense in the sense that all contingent claims on the primary assets must trade in many applications especially with respect to continuous trading models this condition is usually satisfied see duffie 2 and harrison and pliska 9 in the case of stochastically dominated assets this paper shows that the relationship of the assets to the state contingent prices is important in identifying arbitrage opportunities in this sense this paper is related to a recent paper of jagannathan 10 jagannathan studies the relationship of second order stochastic dominance not first order to call option valuation this characterization theorem relating arbitrage opportunities to stochastic dominance should provide a valuable tool in the area of stochastic dominance this theorem specifies conditions under which two assets can be compared using first order stochastic dominance on an individual basis for inclusion in the

third degree stochastic dominance here f x and g x are less than cumulative probability distributionis where x is a continuous or discrete random variable representing the outcome of a prospect the closed interval a b is the sample space of both prospects the integral shown in rule 2 and those shown throughout the paper are stieltjes integrals recall that the stieltjes integral fb f x dg x exists if one of the functions f and g is continuous and the other has finite variation in a b let d1 d2 and d3 be three sets of utility functions x d1 is the set containing all utility functions with 4 x and 1 x continuous and 41 x 0 for all xe a b d2 is the set with x 1 x 2 x continuous and q j x 0 02 x o for all xc a b d3 is the set with x 1 x 2 x 3 x continuous and 1 x 04 2 x o o for all xc a b here 1 x denotes the ith derivative of x hadar and russell proved that rule 1 is valid for all cd1 and rutle 2 is valid for all ed2 the authors point out that the set of probability distributions that can be ordered by means of second degree stochastic dominance is in general larger than that which can be ordered by means of first degree stochastic dominance note that in rule 2 they assume that x is not only an increasing function of x but also exhibits weak global risk aversion a condition guaranteed by requiring the second derivative of x to be nonpositive in this paper a condition which will be called third degree stochastic dominance is considered it is based on the following assumption about the form of the utility function x from a normative point of view one expects the risk premium associated with an uncertain prospect to become smaller the greater is the individual s wealth the plausibility and implications of this assumption h ave been explored by john pratt as well as others the risk premium of an uncertain prospect is that amount by which the certainty equivalent of the prospect differs from its expected value in mathematical terms given the prospect f x with expected value a the corresponding risk premium t is obtained by solving the following equation rb

stochastic dominance and expected utility survey and analysis while stochastic dominance has been employed in various forms as early as 1932 it has only been since 1969 1970 that the notion has been developed and extensively employed in the area of economics finance agriculture statistics marketing and operations research in this survey the first second and third order stochastic dominance rules are discussed with an emphasis on the development in the area since the 1980s

incorporating asymmetric distributional information in robust value at risk optimization value at risk var is one of the most widely accepted risk measures in the financial and insurance industries yet efficient optimization of var remains a very difficult problem we propose a computationally tractable approximation method for minimizing the var of a portfolio based on robust optimization techniques the method results in the optimization of a modified var measure asymmetry robust var arvar that takes into consideration asymmetries in the distributions of returns and is coherent which makes it desirable from a financial theory perspective we show that arvar approximates the conditional var of the portfolio as well numerical experiments with simulated and real market data indicate that the proposed approach results in lower realized portfolio var better efficient frontier and lower maximum realized portfolio loss than alternative approaches for quantile based portfolio risk minimization

money and interest in a cash in advance economy the authors analyze an aggregative general equilibrium model in which the use of money is motivated by a cash in advance constraint applied to purchases of a subset of consumption goods the system is subject to both real and monetary shocks which are economy wide and observed by all they develop methods for verifying the existence of characterizing and explicitly calculating equilibria copyright 1987 by the econometric society

participation in farm commodity programs a stochastic dominance analysis grube correctly argues that mini max and maximax criteria can help analysts determine the interval in which for a given set of preferences there will be changes in the preferred distribution the criteria is of less value when simulations are used to generate distributions without exact a priori knowledge of the random draw of order statistics we will argue that in most cases one can go even further and solve for the specific break even level of risk aversion this should simplify the procedures commonly used to rank risky prospects the author calculates that for the data presented the mini max critical value is 0 000003 for risk preferrers and 0 000002 for risk avoiders he concludes that these are low values when compared to the range originally considered 0 04 to 0 03 since his numbers fall within our range this suggests that our range could have been narrower than it was but clearly our range did contain the values he calculated it is noteworthy that when the smaller coefficients were used the relative rankings of choices remained unchanged grube concludes that kp s results are correct in the sense that they give a correct ranking of the order in which alternatives would be chosen by decision makers with varying absolute risk aversion coefficients since ultimately risk analysts are interested in the relative ranking of risky prospects this would suggest that our results are more robust than the author implies in his remarks while grube has suggested a means of identifying the interval of interest we would argue that in many cases one could go further and solve for the break even level of risk preference the break even level would be that value at which there is a switching in the dominance of one distribution over another using results developed by hammond it should be possible to simplify both the calculation and presentation of stochastic dominance results by solving for the break even level two conditions must be satisfied in order to apply hammond s results first constant risk aversion must be assumed while the use of utility functions exhibiting decreasing risk aversion has been advocated in the theoretical literature and supported somewhat by empirical studies which have assessed utility functions in most applications constant risk aversion is assumed this is largely because wealth data is frequently unavailable or of questionable accuracy thus risk analysts typically assume that a decision maker s utility function can be approximated over the relevant range by a constant risk aversion function such as the negative exponential function u x 1 e ax

on stochastic dominance and decreasing absolute risk averse option pricing bounds merton perrakis and ryan levy and ritchken have established option pricing bounds under first and second stochastic dominance preferences these bounds are particularly important for valuing contingent claims when continuous trading in the claim and or underlying security does not exist this article provides option bounds under higher orders of dominance specifically option bounds are obtained by solving mathematical programs where preference structures on prices are represented by constraints for first second third and higher orders of stochastic dominance preferences the special linear structure of the mathematical programs allow analytical solutions to be obtained for the bounds for dara preferences third order stochastic dominance while being necessary is not sufficient and additional constraints must be imposed unfortunately these additional constraints are nonlinear while in this case closed form analytical solutions for the option bounds are not obtained numerical examples are presented to illustrate their strength

the next round game theory and public choice perspectives abstract the uruguay round of multilateral trade negotiations proved to be unduly lengthy because of the absence of an adequate negotiating framework to resolve complex new issues although solutions have been found for many issues with the conclusion of the round others remain to be addressed and emerging issue will require resolution with a new round scheduled to start relatively soon it is useful to identify a negotiating framework that may hasten future discussions game theory and public choice are used as analytical tools to illustrate various scenarios that may help policy makers and negotiators identify with particular reference to agriculture the likely main issues bargaining positions and possibilities for compromise the complexity of the issues the divergence of positions between countries the absence of a dominant leader in world trade and the emergence of trade and negotiating blocs which lack a unified position are however factors that may make the next round of multilateral trade negotiations as protracted as the uruguay round discussion and research concerning the issues are required to facilitate the negotiation process

a note on income velocity of money in a cash in advance economy with capital a stochastic growth model with money introduced via a cash in advance constraint is used to analyze the behaviour of the income velocity of real monetary balances agents can purchase consumption goods only using government issued money and capital is a credit good the cash in advance constraint may become nonbinding because of the uncertainty about the realization of the state of the economy changes in the income velocity of money due to a precautionary money demand are studied we find that despite the precautionary money demand does not introduce significant changes into the volatility of the income velocity its presence can alter the relationship between the growth rate of money supply and the income velocity

valuing information when risk preferences are nonneutral an application to irrigation scheduling a method for valuing information when risk attitudes are nonneutral is presented the procedure uses simulation and generalized stochastic dominance to value information by level of risk aversion the value of soil water and weather information to irrigators is quantified to illustrate the procedure the empirical results show that additional information has diminishing marginal returns for a given level of risk aversion and that the value of information increases with the level of risk aversion the application demonstrates the importance of valuing information on a whole firm basis when returns to information are related to returns of other firm enterprises and risk preferences are nonneutral

comparison of alternative utility functions in portfolio selection problems this paper examines the effect of alternative utility functions and parameter values on the optimal composition of a risky investment portfolio normally distributed assets are the setting for the theoretical and empirical analyses the results agree well with the available theory and imply utility functions and parameter values that are appropriate for investors with particular risk bearing attitudes the results give strong empirical support to the proposition that utility functions having different functional forms and parameter values but similar absolute risk aversion indices have similar optimal portfolios these results suggest that over horizons up to one year one can safely substitute convenient surrogate utility functions for other utility functions for reasons of tractability or otherwise the results also provide guidance regarding the significance of the magnitude and change of particular numerical values of the risk aversion index moreover theoretical exact results are obtained using rubinstein s measure of global risk aversion

some results on bond yield and default probability fisher 5 suggested that the difference between a corporate bond s promised yield tomaturity ytm and the ytm of a government bond of the same maturity is composed of the sum of the corporate default risk the variability of the firm s earnings the firm s reliability in meeting its obligations its capital structure and the bond s marketability since then fisher s measure has often been used to measure bond risk for example fraser and mccormack 6 have used the spreads between newly issued bank bonds and aaa bonds of compatible maturities as substitutes for riskless government bonds to measure the changes in banks borrowing risk after two large bank failures in their paper spread is intended to provide for intra firm industry default risk comparisons over time radcliffe 15 uses yield spreads to differentiate the riskiness among corporate bonds in this case the spread is used for inter firm risk comparisons sharpe 18 has suggested a similar measure of bond default risk which is the ytm less the expected rate of return however most of these papers do not provide a bond pricing model which would furnish the link between a firm s riskiness and the ytm and default risk of its bond without this it is difficult to draw inferences between ytm s and default risk

choice under uncertainty problems solved and unsolved ffifteen years ago the theory of choice under uncertainty could be considered one of the success stories of economic analysis it rested on solid axiomatic foundations it had seen important breakthroughs in the analytics of risk risk aversion and their applications to economic issues and it stood ready to provide the theoretical underpinnings for the newly emerging information revolution in economics 1 today choice under uncertainty is a field in flux the standard theory is being challenged on several grounds from both within and outside economics the nature of these challenges and of our profession s responses to them is the topic of this paper

stochastic dominance and the investment horizon with riskless assets this paper analyses the relationship between the efficient sets of investment portfolios and the investment holding period investors are allowed to hold risky assets as well as the riskless asset the main result is that dominance in each period implies dominance in the multiperiod case this finding holds with respect to first second and third degree stochastic dominance the riskless interest rate may vary from one period to another without changing the results of this paper

demand for risky financial assets a portfolio analysis abstract demand for risky financial assets takes place in portfolio settings the common stochastic orders applied in economics fail to rank demand for assets in such situations even for risk averse investors therefore the evaluation of the relative desirability of risky financial assets requires the establishment of new orders we prove that if returns on risky assets are ordered by the monotone likelihood ratio order then dominating assets will be more desired by all investors with nondecreasing utility functions

a decision theoretic foundation for reward to risk performance measures abstract in this paper we prove that partial moments based performance measures e g omega kappa upside potential ratio sortino satchell ratio farinelli tibiletti ratio value at risk based performance measures e g var ratio cvar ratio rachev ratio generalized rachev ratio and other admissible performance measures are a strictly increasing function in the sharpe ratio the theoretical basis of this result is the location and scale property and two other plausible and mild conditions our result provides a decision theoretic foundation for all these frequently used performance measures moreover it might explain the empirical finding that all these measures typically lead to very similar rankings

identifying vulnerability to poverty a critical survey in the economic literature on poverty various methods have been proposed for measuring a phenomenon known as vulnerability however after more than a quarter century of research no consensus has been reached on how to identify such vulnerable individuals within a given population some misunderstandings have also arisen from the overlapping of other closely related concepts such as the expectation of being poor expected poverty multi period poverty and risk exposure this paper offers a detailed conceptual discussion on vulnerability to poverty and its related elements reviewing a wide range of identifying criteria provided in the literature it is found that according to the state of the art in this field of research two key elements stand out in identifying vulnerable individuals an expected well being below the poverty line and a relevant risk of falling into poverty due to downside deviation from a reference level of well being the traditional classification of vulnerability approaches has been updated into four groups i those that stress the element of exposure to risk ii those that emphasize the element of expected poverty iii those that define vulnerability through a utility gap and iv those that are supported by a mean risk dominance criterion

on endogenous growth with physical and human capital this paper presents a class of models in which agents may devote part of their nonleisure activities to going to school so as to increase the efficiency units of labor they supply to the firms and the wages they receive the interaction among the technology of human capital accumulation and agents preferences will determine endogenously the economy s rate of growth given a constant returns to scale technology for physical capital accumulation we characterize the set of steady states as a ray from the origin and show the global convergence of every off balanced path to some point on this ray further properties concerning the dynamic evolution of the state and control variables around the ray of steady states are also established our analysis is useful to understand the role played by the technologies of physical and human capital in the process of accumulation and to evaluate the impact of policies geared toward attaining higher levels of capital our results highlight the importance of human capital

a comparative analysis of water price support versus drought compensation scheme abstract this paper examines the preferred governmental intervention towards crops growing methods in semi arid regions these regions are characterized by an average amount of rain which is sufficient to grow the crop but it is also very risky the farmers attitude towards risk motivates the government to encourage them to shift to more profitable and riskier crop rotations the paper analyses two alternatives of which the government can work through drought compensation scheme dcs and water price support wps the semi arid region in israel is analyzed and policy conclusions are derived in particular it is shown that for different sub regions within the semi arid region different mechanisms are preferred by the government and the farmers sometimes these mechanisms coincide and sometimes they do not a welfare analyzes compares the different situations

mean lower partial moment valuation and lognormally distributed returns in this paper we develop a capital asset pricing model in a mean lower partial moment framework specifically we show that when partial moments are computed about the expected risky portfolio return optimal portfolio choice in a mean lower partial framework permits a two fund portfolio separation between a riskless asset and a market portfolio of risky assets in this new framework risk is measured as semideviation for second degree stochastic dominance and semivariance for third degree stochastic dominance further when security returns are lognormally distributed and small risk this new mean lower partial moment valuation specializes to the mean logarithmic variance capital asset pricing model

a note on almost stochastic dominance abstract both the expected utility maximization and the hierarchy property are very important properties in stochastic dominance for almost stochastic dominance leshno and levy 2002 propose a definition and tzeng et al 2013 modified it to give another definition this note provides more information on the two definitions the former has the hierarchy property but not the expected utility maximization whereas the latter has the expected utility maximization but not the hierarchy property

data envelopment analysis models of investment funds abstract this paper develops theory missing in the sizable literature that uses data envelopment analysis to construct return risk ratios for investment funds it explores the production possibility set of the investment funds to identify an appropriate form of returns to scale it discusses what risk and return measures can justifiably be combined and how to deal with negative risks and identifies suitable sets of measures it identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it it identifies relationships between diversification coherent measures of risk and stochastic dominance it shows how the iterative procedure makes a practical difference using monthly returns of 30 hedge funds over the same time period it discusses possible shortcomings of the procedure and offers directions for future research

stochastic dominance analysis without the independence axiom we characterize the consistency of a large class of nonexpected utility preferences including mean variance preferences and prospect theory preferences with stochastic orders for example stochastic dominances of different degrees our characterization rests on a novel decision theoretic result that provides a behavioral interpretation of the set of all derivatives of the functional representing the decision maker s preferences as an illustration we consider in some detail prospect theory and choice acclimating preferences two popular models of reference dependence under risk and we show the incompatibility of loss aversion with prudence this paper was accepted by james smith decision analysis

transfer principles in income redistribution abstract dalton s principle of transfer for income redistribution says that society will be better off when a unit of income in transferred from a richer to a poorer individual this paper investigates the conjunction of a natural extension of dalton s principle which says that any combination of a socially desirable transfer with its inverse at uniformly higher levels of income will have positive social benefit and a traditional utilitarian egalitarian formulation of social welfare the transfer principles involved in the extension of dalton s rule correspond to stochastic dominance relations between income distributions with a common mean and lead to the conclusion that when and g are income distributions the social welfare of is larger than that of g if e ax x ax g x for all positive a this conclusion is intimately connected with a measure of income inequality studied by kolm

asset proportions in optimal portfolios the paper is concerned with conditions under which the proportion of a given asset in the optimal portfolio of a risk averse agent is at least as large as some given proportion the paper provides a condition that is necessary and sufficient for such a result to hold the analysis is then confined to portfolios in which the distributions of assets differ by either a first degree stochastic dominance shift or by a mean preserving shift examples are provided to show that under some conditions a risk averter may invest a smaller proportion of his wealth in the dominating asset than in the dominated asset the paper then provides conditions that are necessary and sufficient for a risk averter to invest more in the dominating asset the question of whether risk averse agents should or should not choose diversified portfolios as opposed to specialized ones has been analysed quite extensively in the literature examples of such works are samuelson 1967 brumelle 1974 hadar and russell 1974 russell and seo 1979 hadar and seo 1980 and macminn 1984 what has not been examined at all except for very special cases is the question of the optimal proportions of the various assets in a diversified portfolio in this paper we present conditions which imply that the optimal amount invested in a particular asset is at least as large as some given proportion of the available fund in the case of two asset portfolios one may especially want to know which of the two assets represents more than half the investible fund indeed we find it convenient to start the analysis with the two asset case while the extension to n asset protfolios is essentially straightfoward it is presented in a subsequent section focusing first on the two asset case will make it easier for the reader to see the main logical steps in the proofs of the theorems some of our analysis is facilitated by the use of a particular subset of risk averters this subset has the property that if its members behave in a particular way then all risk averters behave in that way we refer to such a subset as a representative set of all risk averters 2 the usefulness of the representative set derives from the fact that its members have utility functions of a very simple form consisting of two linear pieces and its applicability to the problems on hand derives from the fact that any concave function can be approximated by a linear combination of members of the representative set in the next section we present some formal results demonstrating the equivalence of unanimity among members of the representative set and unanimity among all risk averters in certain types of choice situations these theorems are then used in section 3 in which we present the results about optimal asset proportions

stochastic dominance and uncertain price prospects since the seminal and simultaneous publications of hadar and russell 6 and hanoch and levy 8 there has been a virtual explosion of papers investigating implications of stochastic dominance rules for decisions under uncertainty dominance principles have important applications to portfolio choice capital budgeting and financial intermediation stochastic dominance can also be applied to investment and production decision problems under uncertainty in these areas both overall and marginal impacts of uncertainty have received wide attention 2 the emphasis in consumer welfare analysis under uncertainty has been on the ranking of different price prospects ranking of price prospects is more complicated than that of income prospects for two related reasons first due to differences in ordinal preferences among consumers the second degree stochastic dominance rule on price prospects does not yield a unanimous ranking among risk averse consumers thus waugh 17 massell 12 and samuelson 14 have focused on the ranking of price prospects for a single consumer or consumers with identical ordinal preferences second there is no a priori reason for income risk averse consumers to exhibit aversion to fair price risks specifically the indirect utility function of an income risk averse consumer is neither concave nor convex in prices indirect ways of comparing consumer welfare under alternative price prospects via expected consumer surplus expected compensating variation or expected equivalent variation have thus been investigated in the literature expected consumer surplus ecs has been particularly popular for ranking certain and uncertain price prospects 3 however turnovsky shalit and schmitz 16 showed that the ranking

developments in biophysical and bioeconomic simulation of agricultural systems a review this paper reviews the features and uses of some recent biophysical and bioeconomic simulation models in agricultural economics research problems associated with earlier models are discussed and the extent to which recent simulators have addressed these concerns is appraised some salient factors that will enhance the continued relevance of simulators as research and decision support tools are indicated