We examine Kreps' (2019) conjecture that optimal expected utility in the classic Black--Scholes--Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies that approach the BSM economy in a natural sense: The $n$th discrete-time economy is generated by a scaled $n$-step random walk, based on an unscaled random variable $\zeta$ with mean zero, variance one, and bounded support. We confirm Kreps' conjecture if the consumer's utility function $U$ has asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility function $U$ with asymptotic elasticity equal to 1, for $\zeta$ such that $E[\zeta^3] > 0.$
Abstract We examine Kreps' conjecture that optimal expected utility in the classic Black–Scholes–Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete‐time economies that “approach” the BSM economy in a natural sense: The n th discrete‐time economy is generated by a scaled n ‐step random walk, based on an unscaled random variable ζ with mean 0, variance 1, and bounded support. We confirm Kreps' conjecture if the consumer's utility function U has asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility function U with asymptotic elasticity equal to 1, for ζ such that .
The analysis of structured countable stage decision processes, initiated in Porteus [11], is continued. The standard models of positive and negative dynamic programming are given in this context, thus extending these results to criteria other than the usual expected sum of rewards, such as expected utility criteria, certain stochastic games, risk sensitive Markov decision processes, and maximin criteria. For positive problems, (what are called) unimprovable strategies are optimal and the optimal value sequence is the least solution of the optimality equations exceeding an obvious lower bound. For negative problems, conserving strategies are optimal, and if one strategy is a one-step improvement on another, then it nets a greater value. (This rules out cycling in the strategy iteration procedure.) Also, transfinite methods are used to prove that the optimal value sequence is the greatest solution of the optimality equations less than an obvious upper bound. We indicate how all these results can be extended to analogues of the essentially positive, essentially negative, and convergent cases.
We examine Kreps' (2019) conjecture that optimal expected utility in the classic Black--Scholes--Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies that "approach" the BSM economy in a natural sense: The $n$th discrete-time economy is generated by a scaled $n$-step random walk, based on an unscaled random variable $\zeta$ with mean zero, variance one, and bounded support. We confirm Kreps' conjecture if the consumer's utility function $U$ has asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility function $U$ with asymptotic elasticity equal to 1, for $\zeta$ such that $E[\zeta^3] > 0.$
This three volume set contains papers presented at the Seventh World Congress of the Econometric Society. The first volume contains three papers presented at the Seventh World Congress of the Econometric Society which summarize and interpret key recent developments and discuss current and future directions in a wide range of topics in economics and econometrics. They cover both theory and applications. Authored by leading specialists in their fields, these volumes provide a unique survey of progress in the discipline. The second volume comprising three papers which examine the latest developments in economic theory, applied economics and econometrics presented at the Seventh World Congress of the Econometric Society in Tokyo in August 1995. The topics were carefully selected to represent the most active fields in the discipline over the past five years. Written by the leading authorities in their fields, each paper provides a unique survey of the current state of knowledge in economics. Designed to make the material accessible to a general audience of economists, these volumes should be helpful to anyone with a good undergraduate training in economics who wishes to follow new ideas and tendencies in the subject. The third of three volumes contains papers presented at the Seventh World Congress of the Econometric Society. The papers summarize and interpret key recent developments and discuss current and future directions in a wide range of topics in economics and econometrics. They cover both theory and applications. Authored by leading specialists in their fields, these volumes provide a unique survey of progress in the discipline.
