a note on merton s optimum consumption and portfolio rules in a continuous time model in the paper optimum consumption and portfolio rules in a continuous time model by r c merton j econ theory 3 1971 373 413 solutions obtained in cases when marginal utility at zero consumption is finite are not feasible while they do satisfy the hamilton jacobi bellman equations they do not represent appropriate value functions because the boundary behavior near zero wealth is not satisfactorily dealt with in this note we specify the boundary behavior and characterize optimal solutions journal of economic literature classification numbers 022 213

an empirical model of labor supply in a life cycle setting this paper formulates and estimates a structural intertemporal model of labor supply using theoretical characterizations derived from an economic model of lifetime behavior a two step empirical analysis yields estimates of intertemporal and uncompensated substitution effects which provide the information needed to predict the response of hours of work to life cycle wage growth and shifts in the lifetime wage path

investment under uncertainty and time inconsistent preferences abstract while standard real options models assume that agents possess a constant rate of time preference there is substantial evidence that agents are impatient about choices in the short term but are patient when choosing between long term alternatives we extend the real options framework to model the investment timing decisions of entrepreneurs with time inconsistent preferences the impact on investment timing depends on such factors as whether entrepreneurs are sophisticated or naive in their expectations regarding their future time inconsistent behavior and whether the payoff from investment occurs all at once or over time the model is extended to the case of a competitive equilibrium

a single period stocking and pricing problem involving stochastic emergency supply abstract we develop a model for determining jointly optimal price and production policy of products with short life cycles subject to partially uncertain supply capacity within the price setting newsvendor framework we consider that demand in excess of the stocking quantity can be met by an emergency order due to the randomness of emergency supply capacity it may not always be possible to satisfy the demand completely assuming that all customers are charged the same price we explore the optimal sourcing and pricing decisions in the commonly used additive and multiplicative demand scenarios the first order conditions imply that the optimal price in the problem with random emergency supply is less than the optimal price associated with the deterministic demand problem when demand uncertainty is additive and it is greater than the optimal price associated with the deterministic demand problem when demand uncertainty is multiplicative we also find that the same type of comparative static applies in the multiplicative uncertainty case when there exists a dual source emergency system consisting of a perfectly reliable supplier and a second supplier with a stochastic capacity

anomalies in intertemporal choice evidence and an interpretation research on decision making under uncertainly has been strongly influenced by the documentation of numerous expected utility eu anomalies behaviors that violate the expected utility axioms the relative lack of progress on the closely related topic of intertemporal choice is partly due to the absence of an analogous set of discounted utility du anomalies we enumerate a set of du anomalies analogous to the eu anomalies and propose a model that accounts for the anomalies as well as other intertemporal choice phenomena incompatible with du we discuss implications for savings behavior estimation of discount rates and choice framing effects

an isomorphism between asset pricing models with and without linear habit formation we show an isomorphism between optimal portfolio selection or competitive equilibrium models with utilities incorporating linear habit formation and corresponding models without habit formation the isomorphism can be used to mechanically transform known solutions not involving habit formation to corresponding solutions with habit formation for example the constantinides 1990 and ingersoll 1992 solutions are mechanically obtained from the familiar merton solutions for the additive utility case without recourse to a bellman equation or first order conditions more generally recent solutions to portfolio selection problems with recursive utility and a stochastic investment opportunity set are readily transformed to novel solutions of corresponding problems with utility that combines recursivity with habit formation the methodology also applies in the context of hindy huang kreps 1992 preferences where our isomorphism shows that the solution obtained by hindy and huang 1993 can be mechanically transformed to dybvig s 1995 solution to the optimal consumption investment problem with consumption ratcheting this article presents a general method for solving asset pricing or portfolio selection models involving linear habit formation of the type studied by sundaresan 1989 constantinides 1990 detemple and zapatero 1991 ingersoll 1992 chapman 1998 and others the basic idea we pursue is that linear habit formation can be thought of as a redefinition of what constitutes consumption to include not only the current consumption rate but also a fictitious possibly negative consumption rate derived from past actual consumption by pricing out this fictitious consumption rate correctly the economy with linear habit formation can be mechanically transformed to an equivalent economy without habit formation this analysis simplifies and unifies existing results but also generates novel solutions for example together with the results of schroder and skiadas 1997 1999 our method produces optimal lifetime consumption and portfolio policies with preferences that combine recursive utility with habit formation under a stochastic

continuous time methods in finance a review and an assessment i survey and assess the development of continuous time methods in finance during the last 30 years the subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing term structure theory asset pricing and optimal consumption and portfolio choices during the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance this latter subperiod has seen significant progress in econometric theory computational and estimation methods to test and implement continuous time models capital market frictions and bargaining issues are being increasingly incorporated in continuous time theory the roots of modern continuous time methods in finance can be traced back to the seminal contributions of merton 1969 1971 1973b in the late 1960s and early 1970s merton 1969 pioneered the use of continuous time modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting merton 1973b also showed how such a framework can be used to develop equilibrium asset pricing implications thereby significantly extending the asset pricing theory to richer dynamic settings and expanding the scope of applications of continuous time methods to study problems in financial economics 1 within a span of about 30 years from the publication of merton s inf luential papers continuous time methods have become an integral part of financial economics indeed in certain core areas in finance such as e g asset pricing derivatives valuation term structure theory and portfolio selection continuoustime methods have proved to be the most attractive way to conduct research and gain economic intuition the continuous time approach in these areas has produced models with a rich variety of testable implications the econometric theory for testing continuous time models has made rapid strides in the last decade and has thus kept pace with the impressive progress on the theoretical front one hopes that the actual empirical investigations and estimation using the new procedures will follow suit soon

strategic real options under asymmetric information abstract this paper studies the effect of private information on the capital allocation decisions of firms who operate under imperfect competition i analyze two interactive firms one with private information and the other without who must decide when to undertake an irreversible and uncertain investment decision traditional non strategic models of irreversible investment under uncertainty involve a single decision maker and result in an optimal period of delay before the investment is undertaken in a strategic setting firms must balance their desire to delay against competitive advantages from early investment i find that an equilibrium may not exist within the standard continuous framework when the private information is over revenues moreover when an equilibrium does exist the competitive pressures from the uninformed firm are weak this is in contrast to existing models with asymmetric information over costs where an equilibrium always exists and the competitive pressures remain strong hsu and lambrecht 2007 this work shows that the investment timing decision and thus the value of the private information is highly sensitive to the nature of incomplete information

role of risk aversion in price postponement under supply random yield price postponement is an effective mechanism to hedge against the adverse effect of supply random yield however its effectiveness and the resulting production decisions have not been studied for

optimal capital structure and investment decisions under time inconsistent preferences based on a continuous time model of quasi hyperbolic discounting this paper provides an analytically tractable framework of entrepreneurial firms capital structure and investment decisions under time inconsistent preferences inefficiency in both investment and default is caused due to time inconsistency if we view the time consistent benchmark as efficient compared to the standard trade off theory in corporate finance we clarify that debt financing under time inconsistent preferences brings a new trade off between the alleviation effect on investment inefficiency and the aggravation effect on default inefficiency the impact of time inconsistent preferences depends on the entrepreneurs belief regarding their future time inconsistent behavior i e sophisticated or naive concretely we find that naive entrepreneurs always choose higher leverages while sophisticated ones are more likely to choose lower leverages compared to the time consistent benchmark therefore time inconsistency can explain the observed leverage puzzle i e why firms choose different leverages even with similar fundamentals moreover we demonstrate that time inconsistent preferences delay investment and hasten default due to the interaction among the three effects option value effect payoff value effect and leverage effect in particular naive entrepreneurs invest later and default earlier than sophisticated ones leading to a shorter operating period these results support the empirical findings in entrepreneurial finance

on the exploitation of additional duality relationships in consumer demand analysis abstract this paper advocates more extensive use of the frisch profit function in static consumer demand studies and intorduces its inverse the price of utility function paralleling the well known relationships between indirect utility and expenditure functions an examination of the relationship between these four functions suggests i a fourth system complementing marshallian hicksian and frisch demand systems and ii a fourth theorem complementing roy s identity shephard s theorem and hoteling s lemma

real option duopolies with quasi hyperbolic discounting abstract this paper utilizes a real options and game theoretic approach to consider the strategic real investment in a duopoly market under uncertainty with time inconsistent preferences resulting from quasi hyperbolic discounting we show that the time consistent agent becomes the leader when s he interacts with a time inconsistent rival if the rival s time inconsistency is very significant the leader will optimally behave as if competition did not exist if the two rivals have about the same time preferences the leader will accelerate investment and her his investment threshold will accord with the rival s preemptive one which is higher than that determined in the classical time consistent model the inefficiency of investment from preemptive competition is mitigated and even eliminated if the heterogeneity among agents is sufficiently high our model provides a behavioral explanation for the empirical fact that preemption occurs in some markets but is not present in others

optimal consumption and portfolio policies when asset prices follow a diffusion process abstract we consider a consumption portfolio problem in continuous time under uncertainty a martingale technique is employed to characterize optimal consumption portfolio policies when there exist nonnegativity constraints on consumption and on final wealth we also provide a way to compute and verify optimal policies our verification theorem for optimal policies involves a linear partial differential equation unlike the nonlinear partial differential equation of dynamic programming the relationship between our approach and dynamic programming is discussed we demonstrate our technique by explicitly computing optimal policies in a series of examples in particular we solve the optimal consumption portfolio problem for hyperbolic absolute risk aversion utility functions when the asset prices follow a geometric brownian motion the optimal policies in this case are no longer linear when nonnegativity constraints on consumption and on final wealth are included by these examples one can see that our approach is much easier than the dynamic programming approach

investment uncertainty and pre emption this paper examines irreversible investment in a project with uncertain returns when there is an advantage to being the first to invest and externalities to investing when others also do so we show that the possibility of pre emption can have significant qualitative and quantitative effects on the relationship between uncertainty and investment in a single agent real options model the trigger threshold for investment increases without bound as uncertainty grows in contrast the investment trigger of a leader faced with pre emption is bounded above as uncertainty increases in fact we show that under certain parameter values greater uncertainty can lead the leader to invest earlier these findings reinforce the importance of extending real options analysis to include strategic interactions between players applications to industry situations are also discussed

valuation optimal asset allocation and retirement incentives of pension plans we provide a framework in which we link the valuation and asset allocation policies of defined benefits plans with the lifetime marginal productivity schedule of the worker and the pension plan formula in turn we examine the retirement policies that are implied by the primitives of the model and the value of pension obligations our model provides an explicit valuation formula for a stylized defined benefits plan the optimal asset allocation policies consist of the replicating portfolio of the pension liabilities and the growth optimum portfolio independent of the pension liabilities we show that the worker will retire when the ratio of pension benefits to current wages reaches a critical value which depends on the parameters of the pension plan and the discount rate using numerical techniques we analyze the feedback effect of retirement policies on the valuation of plans and on the asset allocation decisions article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

real options and preemption under incomplete information abstract this paper introduces incomplete information and preemption into an equilibrium model of firms facing real investment decisions the optimal investment strategy may lie anywhere between the zero npv trigger level and the optimal strategy of a monopolist depending on the distribution of competitors costs and the implied fear of preemption our model implies that the equity returns of firms which hold real options and are subject to preemption will contain jumps and positive skewness

towards a more general approach to testing the time additivity hypothesis a new procedure is proposed for re examining the assumption of additivity of preferences over time which although untenable is usually maintained in intertemporal analyses of consumption and labour supply the method is an extension of a famous work by browning however it is more general in permitting the estimation of intertemporal demand systems which are explicit in an unobservable variable price of utility but may lack a closed form representation in terms of observable variables such as prices and total outlay it also makes extensive use of duality theory to solve the endogeneity problem encountered in browning s study applying this method with an appropriate estimator to the australian aggregate data it is found that the time additivity hypothesis is decisively rejected which is consistent with browning s conclusion

optimal consumption wealth relationships derived by consumer intertemporal profit maximisation abstract this paper proposes an artificial intertemporal consumer profit maximisation problem that is simple to solve the optimal consumption function which is consistent with intertemporal utility maximisation is then generated directly from a specification of the consumer s instantaneous profit function

an intertemporal general equilibrium asset pricing model the case of diffusion information this paper provides sufficient conditions for the equilibrium price system and a vector of exogenously specified state variable processes to form a diffusion process in a pure exchange economy the conditions involve smoothness of agents utility functions and certain nice properties of the aggregate endowment process and the dividend processes of traded assets in place of the dynamic programming a martingale representation technique is utilized to characterize equilibrium portfolio policies this technique is useful even when there does not exist a finite dimensional markov structure in the economy and thus the markovian stochastic dynamic programming is not applicable a gents are shown to hold certain hedging mutual funds and the riskless asset in contrast to earlier results the market portfolio does not have a special role in hedging since the markets are dynamically complete when there exists a finite dimensional markov system in the economy the dimension of the hedging demand identified through the markovian dynamic programming may be much larger than that identified by the martingale method copyright 1987 by the econometric society

dynamic asset allocation in a mean variance framework the aim of this article is to analyze the portfolio strategies that are mean variance efficient when continuous rebalancing is allowed between the current date 0 and the horizon t under very general assumptions when a zero coupon bond of maturity t exists the dynamic efficient frontier is a straight line the slope of which is explicitly characterized every dynamic mean variance efficient strategy can be viewed as buy and hold combinations of two funds the zero coupon bond of maturity t and a continuously rebalanced portfolio an appropriate dynamic strategy defining the latter is explicitly derived for two particular price processes and comparisons of the efficient frontiers static versus dynamic are provided in these cases

two trees with heterogeneous beliefs spillover effect of disagreement in a model where investors disagree about the fundamentals of two stocks the state price density depends on investor disagreements for both stocks especially the larger stock this implies that disagreement among investors in a large firm has a spillover effect on the pricing of other stocks owned by these investors the pricing effects of investor disagreements crucially depend on the average belief biases empirical findings support the novel model prediction of a disagreement spillover effect and help reconcile some mixed evidence in the literature

consumption and portfolio choice under internal multiplicative habit formation this paper explores the optimal consumption and investment behavior of an individual who derives utility from the ratio between his consumption and an endogenous habit we obtain closed form policies under general utility functionals and stochastic investment opportunities by developing a nontrivial linearization to the budget constraint this enables us to explicitly characterize how habit formation affects the marginal propensity to consume and optimal stock bond investments we also show that in a setting that combines habit formation with epstein zin utility consumption no longer grows at unrealistically high rates at high ages and investments in risky assets decrease

technical note optimal product pricing and component production quantities for an assembly system under supply uncertainty we consider an assemble to order system where one of the components faces uncertainty in the supply process in which the actual available quantity is equal to some random fraction of the production quantity demand is assumed to be price dependent we analyze how the supply uncertainty of one component affects the product pricing and production quantities of all the components under the assembly structure we show that it is profitable for the firm to assemble the product only if the product price exceeds a certain threshold this price threshold increases as the unit cost of each component or the degree of variability of the supply reliability distribution increases but it is independent of the underlying demand function and demand distribution also the optimal product price decreases as supply uncertainty decreases we further show that under deterministic demand the components can be managed independently such that the production quantity or unit cost of the component with supply uncertainty does not affect the optimal production quantity of the other components as long as it is profitable to assemble the product however when demand is stochastic the optimal production quantity of each component depends on the supply reliability distribution as well as the unit costs of the other components for a fixed product price the optimal production quantities of the components are smaller when the unit product price is low and they are higher when the unit product price is high as compared to the case with no supply uncertainty

developing real option game models by mixing concepts from both game theoretic analysis and real options theory an investment decision in a competitive market can be seen as a game between firms as firms implicitly take into account other firms reactions to their own investment actions we review two decades of real option game models suggesting which critical problems have been solved by considering game theory and which significant problems have not been yet adequately addressed we provide some insights on the plausible empirical applications or shortfalls in applications to date and suggest some promising avenues for future research

strategic investment timing under asymmetric access charge regulation in telecommunications in a liberalized telecommunications market an incumbent has several advantages over any entrant an asymmetric access charge regulation for two such asymmetric firms stimulates competitive investment we show that an entrant with a cost disadvantage has an incentive to invest as a leader under an asymmetric access charge regulation these results fit well with the findings of previous empirical work moreover we also investigate the effects of an asymmetric access charge regulation on competitive investment strategies

strategic investment in technological innovations abstract the aim of this paper is to determine the optimal timing of technology investment of a single firm in a duopoly framework as time passes different technologies are invented which after sometime become available for the firm to adopt the question here is not only when a firm should invest but also which technology should be adopted for different scenarios the optimal technology investment decision is determined outcomes range from pre emption equilibria to equilibria with second mover advantages

real options in strategic investment games between two asymmetric firms abstract this paper examines strategic investment games between two firms that compete for optimal entry in a project that generates uncertain revenue flows under asymmetry on both the sunk cost of investment and revenue flows of the two competing firms we investigate the value of real investment options and strategic interaction of investment decisions compared to earlier models that only allow for asymmetry on sunk cost our model demonstrates a richer set of strategic interactions of entry decisions we provide a complete characterization of pre emptive dominant and simultaneous equilibriums by analyzing the relative value of leader s and follower s optimal investment thresholds in a duopoly market with negative externalities a firm may reduce loss of real options value by selecting appropriate pre emptive entry when one firm has a dominant advantage over its competitor both the dominant firm and dominated firm enter at their respective leader s and follower s optimal thresholds when the pre emptive thresholds of both firms happen to coincide the two firms enter simultaneously under positive externalities firms do not compete to lead