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

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  • Kreps, David M.

    (Stanford University)

  • Schachermayer, Walter

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.

Suggested Citation

  • Kreps, David M. & Schachermayer, Walter, 2019. "Convergence of Optimal Expected Utility for a Sequence of Discrete-Time Markets," Research Papers 3802, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:3802
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    Cited by:

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    2. Friedrich Hubalek & Walter Schachermayer, 2020. "Convergence of Optimal Expected Utility for a Sequence of Binomial Models," Papers 2009.09751, arXiv.org.
    3. 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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