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

analytical upper bounds for american option prices american options require numerical methods namely lattice models to provide accurate price estimates the computations can become expensive when more than one state variable is involved analytical upper bounds can therefore provide a useful guideline for how high american values can reach in this paper we derive analytical closed form upper bounds for american option prices under stochastic interest rates stochastic volatility and jumps where american option prices are difficult to compute with accuracy in a stochastic volatility model heston 1993 and scott 1997 that has two random factors we demonstrate that the upper bound only takes a very small fraction of the time that the american option needs to compute

valuing catastrophe derivatives under limited diversification a stochastic dominance approach abstract we present a new approach to the pricing of catastrophe event cat derivatives that does not assume a fully diversifiable event risk instead we assume that the event occurrence and intensity affect the return of the market portfolio of an agent that trades in the event derivatives based on this approach we derive values for a cat option and a reinsurance contract on an insurer s assets using recent results from the option pricing literature we show that the assumption of unsystematic event risk seriously underprices the cat option last we present numerical results for our derivatives using real data from hurricane landings in florida

quote inefficiency in options markets in an arbitrage free economy with non zero bid ask spreads the existence of payoffs whose price is lower than the price of a dominated payoff cannot be discarded in general however when the former price corresponds to trivial portfolios which involve buying or selling one unit of the basis assets its presence although not an arbitrage is a severe market anomaly which we refer to as an inefficient quote in an empirical study we report evidence that indicates that in options markets both the frequency and the magnitude of these anomalies are substantial and we document puzzling patterns in their behavior

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

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

robust stochastic discount factors when the market is incomplete a new non redundant derivative security cannot be priced by no arbitrage arguments alone moreover there will be a multiplicity of stochastic discount factors and each of them may give a different price for the new derivative security this paper develops an approach to the selection of a stochastic discount factor for pricing a new derivative security the approach is based on the idea that the price of a derivative security should not vary too much when the payoff of the primitive security is slightly perturbed i e the price of the derivative should be robust to model misspecification the paper develops two metrics of robustness the first is based on robustness in expectation the second is based on robustness in probability and draws on tools from the theory of large deviations we show that in a stochastic volatility model the two metrics yield analytically tractable bounds for the derivative price as the underlying stochastic volatility model is perturbed the bounds can be readily used for numerical examination of the sensitivity of the price of the derivative to model misspecification

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

decreasing absolute risk aversion and option pricing bounds in this paper efficient bounds for the price of a call option are obtained using the decreasing absolute risk aversion dara dominance rule such lower and upper bounds are obtained minimizing and maximizing respectively the objective function of a nonlinear optimization problem an explicit formula related to an exponential utility function is given for the special case of three states of nature a large number of experiments have been carried out and the numerical results support the conjecture that the same formula holds for problems with a number of states n 3 moreover dara bounds are more efficient than the bounds obtained using different criteria

labour supply estimation and public policy abstract economists devote considerable energies towards refining their econometric techniques to overcome difficulties connected with conducting empirical research despite advances in technique it is not clear whether further refinement in this direction is worthwhile for policy purposes it may be that no further amount of statistical adjustment of inadequate data will increase understanding and that better data is simply necessary to add to our knowledge but rarely is sufficient credit paid to new forms of data in short econometric technique is emphasized to the neglect of data innovation as if new data were merely lying about waiting for an ingenious suggestion for use this paper surveys advances of the last twenty five years in estimating labour supply for policy purposes with a view towards appreciating the relative contribution of both improvements in econometric technique as well as developments of new data after briefly detailing the key parameters which economists have sought to estimate we describe the early first generation research circa 1970 which is plagued by problems of unobservable variables measurement errors truncation and selectivity bias and non linear budget constraints second generation research constitute attempts to resolve one or more of these difficulties and the respective contribution of econometric technique and new data is acknowledged and assessed including the contribution of data generated by large scale social experiments in which participants are randomly assigned to different guaranteed income plans and their labour supply behaviour measured

bounds on contingent claims based on several assets abstract in 1987 lo derived an upper bound on the price of a european call option on a single asset lo s bound depends only on the mean and variance of the terminal asset price and is termed a semi parametric bound this paper derives similar semi parametric bounds on a european call on the maximum of any number of assets a distribution free bound for the price of this option is obtained the bound depends only on the means and covariance matrix of the returns on n underlying assets the bound is obtained by optimizing over the entries of a positive definite matrix a this can be accomplished by a technique known as semidefinite programming we demonstrate the methodology using two specific applications the first concerns the valuation of a european call option on the maximum of several assets this is known as an outperformance option and is of some practical interest the second application concerns the valuation of a discretely adjusted lookback option these lookback options are of interest in connection with certain equity annuity insurance products

option prices and the underlying asset s return distribution this work examines the relation between option prices and the true as opposed to risk neutral distribution of the underlying asset if the underlying asset follows a diffusion with an instantaneous expected return at least as large as the instantaneous risk free rate observed option prices can be used to place bounds on the moments of the true distribution an illustration of the paper s results is provided by the analysis of the information concerning the mean and standard deviation of market returns contained in the prices of s p 100 index options although it seems natural that the prices of claims to various parts of the underlying asset s distribution should contain information about the shape of that distribution cox and ross 1976 established that an option s price equals its expected payoff discounted at the risk free rate where the expectation is taken over the risk neutral rather than the true distribution of the underlying asset linking the risk neutral distribution implicit in option prices to the true distribution remains a comparative mystery a necessary condition for the risk neutral pricing methodology to be applicable is that the true and the risk neutral distribution share a common support the only information about the true distribution that can be obtained from observed option prices alone is information about that support this paper demonstrates though that observed option prices when used in conjunction with simple assume d restrictions on the true distribution do contain information about the noncentral moments of the true distribution not directly implied by those assumed restrictions alone the intuition for the result that option prices can be useful in placing bounds on the moments of the true distribution is straightforward first we generalize the results in lo 1987 to show how the expected payoff to a call can be bounded above in terms of any chosen set of the noncentral moments of the return on the underlying asset second we establish restrictions on the

on the mean variance tradeoff in option replication with transactions costs this paper analyzes the tradeoff between cost and risk of discretely rebalanced option hedges in the presence of transactions costs i present closed form solutions for expected hedging error transactions costs and variance of the cash flow from a time based hedging strategy similar to that analyzed by leland 1985 furthermore i characterize the cost and risk of a move based hedging strategy without resorting to monte carlo simulations all results are sufficiently general to accommodate the use of a transactions costs adjusted hedging volatility and an asset rate of return that differs from the risk free rate of return

option replication in discrete time with transaction costs option replication is discussed in a discrete time framework with transaction costs the model represents an extension of the cox ross rubinstein binomial option pricing model to cover the case of proportional transaction costs the method proceeds by constructing the appropriate replicating portfolio at each trading interval numerical values of these prices are presented for a range of parameter values the paper derives a simple black scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values

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

economic response to a guaranteed annual income experience from canada and the united states this article reviews research from the five income maintenance experiments in canada and the united states after sketching the historical and political context of the experiments we compare their designs and discuss some important analytic difficulties our primary focus is the work incentive issue both nonstructural estimates of the experimental effects and elasticity estimates of structural labor supply functions we provide initial estimates of nonstructural and structural models for the canadian experiment we discuss more briefly some non work response findings associated with a guaranteed annual income and offer some personal comments on social experimentation and the policy process

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

third order extensions of lo s semiparametric bound for european call options computing semiparametric bounds for option prices is a widely studied pricing technique in contrast to parametric pricing techniques such as monte carlo simulations semiparametric pricing techniques do not require strong assumptions about the underlying asset price distribution we extend classical results in this area specifically we derive closed form semiparametric bounds for the payoff of a european call option given up to third order moment i e mean variance and skewness information on the underlying asset price we analyze how these bounds tighten the corresponding bounds when only second order moment i e mean and variance information is provided we describe applications of these results in the context of option pricing as well as in other areas such as inventory management and actuarial science

leverage constraints and the optimal hedging of stock and bond options this paper considers the problem of a financial institution that needs to hedge a stream of state contingent cash flows while facing borrowing and short sales restrictions the study determines analytically the strategy that minimizes the initial cost of hedging the desired cash flow which is also the upper bound on its market price and shows that the impact of leverage constraints on the cost of hedging call and put options is significant and therefore the biases detected by tests of option pricing models may not represent arbitrage opportunities the paper also shows that with credit limits it is optimal to reduce the rate of trading thus these constraints need to be recognized when estimating the trading volume generated in replicating contingent payoffs such as portfolio insurance

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

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

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

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

the global financial crisis and the european single market the end of integration using various versions of the feldstein horioka fh coefficient we measure the time varying degree of capital mobility and economic integration in the european union prior research shows high correlation between domestic investment and savings implying low capital mobility this surprising result has led to subsequent research on the feldstein horioka puzzle our empirical findings show that the puzzle is less puzzling with a coefficient of 0 52 in the period 1990 1995 in eu countries approaching its minimum value of 0 02 in the period 2003 2008 this clearly indicates that the fh coefficient is time varying signalling a deepening of economic integration in the european union yet with the advent of the global financial crisis the fh coefficient has increased to 0 26 underlining worrying signs of disintegration

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

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

making inferences from controlled income maintenance experiments nationally this paper addresses a question whose answer is essential for interpreting the results of such experiments if an experiment of limited duration is conducted under ideal conditions what can be inferred from the experimental results about behavior in a world where nit is adopted permanently by ideal conditions we mean that a individuals or households 2 in the experiment are conventional utility maximizers given the structure of the experiment and b the experiment is sufficiently well designed to permit the differential responses of individuals to be identified 3 the

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

semi parametric upper bounds for option prices and expected payoffs abstract upper bounds on the expected payoff of call and put options are derived these bounds depend only on the mean and variance of the terminal stock price and not on its entire distribution so they are termed semi parametric a corollary of this result is a set of upper bounds for option prices obtained by the risk neutral valuation approach of cox and ross as an example these bounds are shown to obtain across both lognormal diffusions and mixed diffusion jump processes for any given data set we present an illustrative example that suggests these bounds may be of considerable practical value

recovering an asset s implied pdf from option prices an application to crude oil during the gulf crisis we develop a general method for estimating the implied martingale equivalent probability density function pdf for futures prices from american options prices the early exercise feature of american options precludes expressing the price of the option in terms of the pdf there exist tight bounds for the price of american options in terms of the pdf we demonstrate how these bounds together with observed option prices can be used to estimate the parameters of the pdf we estimate the distribution for crude oil during the persian gulf crisis and find the distribution differs significantly from that recovered using standard techniques

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

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

option pricing bounds with standard risk aversion preferences abstract for a theoretical valuation of a financial option various models have been proposed that require specific hypotheses regarding both the stochastic process driving the price behaviour of the underlying security and market efficiency when some of these assumptions are removed we obtain an uncertainty interval for the option price up to now the most restrictive intervals for option prices have been obtained using the decreasing absolute risk aversion dara rule in a state preference approach precautionary saving entails the concept of prudence in particular decreasing absolute prudence is a necessary and sufficient condition that guarantees that the saving of wealthier people is less sensitive to the risk associated to future incomes if this condition is coupled with the dara assumption we obtain standard risk aversion sra which guarantees on the one hand that introducing a zero mean background risk to wealth makes people less willing to accept another independent risk and on the other hand that an increase in the risk of the returns distribution of an asset reduces the demand for this asset the main idea of this contribution is to apply decreasing absolute prudence and sra rules in a state preference context in order to obtain efficient bounds for the value of european style options portfolio strategies lower and upper bounds for the options portfolio value are obtained by solving non linear optimization problems the numerical experiments carried out show the efficiency of the technique proposed

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

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

capital mobility and the relationship between saving and investment rates in oecd countries abstract this paper considers tests that use data on saving and investment rates to determine the degree of international capital mobility two types of evidence are presented to show that a high correlation between saving and investment rates across oecd countries can be consistent with a high degree of capital mobility this evidence qualifies the conclusions of previous studies and casts doubt on the usefulness of testing hypotheses about capital mobility with data on saving and investment rates

tight bounds on american option prices in contrast to the constant exercise boundary assumed by broadie and detemple 1996 broadie m detemple j 1996 american option valuation new bounds approximations and comparison of existing methods review of financial studies 9 1211 1250 we use an exponential function to approximate the early exercise boundary then we obtain lower bounds for american option prices and the optimal exercise boundary which improve the bounds of broadie and detemple 1996 with the tight lower bound for the optimal exercise boundary we further derive a tight upper bound for the american option price using the early exercise premium integral of kim 1990 kim i j 1990 the analytic valuation of american options review of financial studies 3 547 572 the numerical results show that our lower and upper bounds are very tight and can improve the pricing errors of the lower bound and upper bound of broadie and detemple 1996 by 83 0 and 87 5 respectively the tightness of our upper bounds is comparable to some best accurate efficient methods in the literature for pricing american options moreover the results also indicate that the hedge ratios deltas and gammas of our bounds are close to the accurate values of american options

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

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

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

bounds and prices of currency cross rate options abstract this paper derives the pricing bounds of a currency cross rate option using the option prices of two related dollar rates via a copula theory and presents the analytical properties of the bounds under the gaussian framework our option pricing bounds are useful because 1 they are general in the sense that they do not rely on the distribution assumptions of the state variables or on the selection of the copula function 2 they are portfolios of the dollar rate options and hence are potential hedging instruments for cross rate options and 3 they can be applied to generate bounds on deltas the empirical tests suggest that there are persistent and stable relationships between the market prices and the estimated bounds of the cross rate options and that our option pricing bounds obtained from the market prices of options on two dollar rates and the historical correlation of two dollar rates are highly informative for explaining the prices of the cross rate options moreover the empirical results are consistent with the predictions of the analytical properties under the gaussian framework and are robust in various aspects

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

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

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

equilibrium pricing in incomplete markets given the exogenous price process of some assets we constrain the price process of other assets that are characterized by their final payoffs we deal with an incomplete market framework in a discrete time model and assume the existence of the equilibrium in this setup we derive restrictions on the state price deflators these restrictions do not depend on a particular choice of utility function we investigate numerically a stochastic volatility model as an example our approach leads to an interval of admissible prices that is more robust than the arbitrage pricing interval

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

option pricing and replication with transactions costs transactions costs invalidate the black scholes arbitrage argument for option pricing since continuous revision implies infinite trading discrete revision using black scholes deltas generates errors which are correlated with the market and do not approach zero with more frequent revision when transactions costs are included this paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision hedging errors are uncorrelated with the market and approach zero with more frequent revision the technique permits calculation of the transactions costs of option replication and provides bounds on option prices

is full banking integration desirable abstract we analyze the links between banking integration and economic development for a sample of oecd countries we measure banking integration considering indicators that merge not only openness but also connectedness with other banking systems we plug these indicators into income regressions also controlling for other relevant variables considered by the literature in contrast to previous initiatives this second stage explicitly takes into account the differing levels of economic development of the countries in our sample since the benefits of enhanced banking integration might not be generalizable to this end we implement quantile regression also considering the presence of endogenous regressors results show that bank connectedness is more important for economic development than bank openness but the combined effect i e banking integration overall is positive and significant the quantile regression models used in the second stage show that the effects are stronger for the poorest economies

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

optimal replication of options with transactions costs and trading restrictions this paper analyzes the strategy that minimizes the initial cost of replicating a contingent claim in a market with transactions costs and trading constraints the linear programming and two stage backward recursive models developed are applicable to the replication of convex as well as nonconvex payoffs and to a portfolio of options with different maturities the paper s formulation conveniently accounts for fixed and variable transactions costs lot size constraints and position limits on trading the article shows that in the presence of trading frictions it is no longer optimal to revise one s portfolio in each period at the optimum cash flows in excess of the desired ones may be generated the optimal policy trades off the curvature of the payoff that is generated against the terminal slack

stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs by applying stochastic dominance arguments upper bounds on the reservation write price of european calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security the primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option a tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put these results jointly impose tight upper and lower bounds on the implied volatility

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

the labor supply response of twenty year families in the denver income maintenance experiment this paper presents results of an analysis of the labor supply response of 20 year families in the denver income maintenance experiment the results indicate that 20 year husbands and wives do not reduce their labor supply relative to control families while 20 year single female heads of families reduce their labor supply by about the same amount as similar families on the 3and 5 year programs the results suggest that the limited duration of the 3and 5 year experiments may not have caused major biases in the estimated treatment effects although the imprecise estimates resulting from the small sample sizes of the 20 year experiment greatly qualify this conclusion

vignettes on the world capital market this paper is motivated by a sense that we as a profession need to understand much better than we now do how the world capital market works we seem to be genuinely schizophrenic in the ways we build models many of them are closedeconomy models in which the rest of the world does not even appear yet others of them are models of the small open economy in which hardly any degree of freedom is left for economic policy to influence events lying behind the schizophrenia is i believe a genuine ignorance on our collective part of how the world capital market

stochastic dominance and expected utility 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

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

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

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

generalized analytical upper bounds for american option prices this paper generalizes and tightens chen and yeh s 2002 analytical upper bounds for american options under stochastic interest rates stochastic volatility and jumps where american option prices are difficult to compute with accuracy we first generalize theorem 1 of chen and yeh 2002 and apply it to derive a tighter upper bound for american calls when the interest rate is greater than the dividend yield our upper bounds are not only tight but also converge to accurate american call option prices when the dividend yield or strike price is small or when volatility is large we then propose a general theorem that can be applied to derive upper bounds for american options whose payoffs depend on several risky assets as a demonstration we utilize our general theorem to derive upper bounds for american exchange options and american maximum options on two risky assets

on the equality of two lower bounds on the call price a note this note shows that appearances to the contrary the lower bounds on the price of a call option obtained by levy and by ritchken are identical and that this common bound is never inferior to the lower bound obtained by perrakis and ryan

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