Convergence of Optimal Expected Utility for a Sequence of Discrete-Time Markets

David Kreps and Walter Schachermayer
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Research Papers from Stanford University, Graduate School of Business

Abstract: 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 nth 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.

Date: 2019-07
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Related works:
Journal Article: Convergence of optimal expected utility for a sequence of discrete‐time markets (2020)
Working Paper: Convergence of Optimal Expected Utility for a Sequence of Discrete-Time Markets (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:ecl:stabus:3802

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