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Convergence of optimal expected utility for a sequence of discrete‐time markets

David Kreps and Walter Schachermayer

Mathematical Finance, 2020, vol. 30, issue 4, 1205-1228

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 nth 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 E[ζ3]>0.

Date: 2020
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Citations: View citations in EconPapers (2)

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https://doi.org/10.1111/mafi.12277

Related works:
Working Paper: Convergence of Optimal Expected Utility for a Sequence of Discrete-Time Markets (2020) Downloads
Working Paper: Convergence of Optimal Expected Utility for a Sequence of Discrete-Time Markets (2019) Downloads
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