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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https://doi.org/10.1111/mafi.12277
Related works:
Working Paper: 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 (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathfi:v:30:y:2020:i:4:p:1205-1228
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