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

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  • David M. Kreps
  • Walter Schachermayer

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.

Suggested Citation

  • David M. Kreps & Walter Schachermayer, 2020. "Convergence of optimal expected utility for a sequence of discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1205-1228, October.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:4:p:1205-1228
    DOI: 10.1111/mafi.12277
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    Cited by:

    1. Friedrich Hubalek & Walter Schachermayer, 2020. "Convergence of Optimal Expected Utility for a Sequence of Binomial Models," Papers 2009.09751, arXiv.org.
    2. Friedrich Hubalek & Walter Schachermayer, 2021. "Convergence of optimal expected utility for a sequence of binomial models," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1315-1331, October.

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