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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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    References listed on IDEAS

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    1. Erhan Bayraktar & Leonid Dolinskyi & Yan Dolinsky, 2020. "Extended weak convergence and utility maximisation with proportional transaction costs," Finance and Stochastics, Springer, vol. 24(4), pages 1013-1034, October.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Erhan Bayraktar & Yan Dolinsky & Jia Guo, 2018. "Continuity of Utility Maximization under Weak Convergence," Papers 1811.01420, arXiv.org, revised Jun 2020.
    4. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    5. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
    6. Christian Reichlin, 2016. "Behavioral Portfolio Selection: Asymptotics And Stability Along A Sequence Of Models," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 51-85, January.
    7. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    8. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    9. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    10. Oleksii Mostovyi & Mihai Sîrbu, 2019. "Sensitivity analysis of the utility maximisation problem with respect to model perturbations," Finance and Stochastics, Springer, vol. 23(3), pages 595-640, July.
    11. He, Hua, 1991. "Optimal consumption-portfolio policies: A convergence from discrete to continuous time models," Journal of Economic Theory, Elsevier, vol. 55(2), pages 340-363, December.
    12. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    14. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. 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.
    2. Friedrich Hubalek & Walter Schachermayer, 2020. "Convergence of Optimal Expected Utility for a Sequence of Binomial Models," Papers 2009.09751, arXiv.org.

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