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Continuity of Utility Maximization under Weak Convergence

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  • Erhan Bayraktar
  • Yan Dolinsky
  • Jia Guo

Abstract

In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally, we apply our results to the computation of the minimal expected shortfall (shortfall risk) in the Heston model by building an appropriate lattice approximation.

Suggested Citation

  • Erhan Bayraktar & Yan Dolinsky & Jia Guo, 2018. "Continuity of Utility Maximization under Weak Convergence," Papers 1811.01420, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:1811.01420
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    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.
    4. Cohen, Asaf & Saha, Subhamay, 2021. "Asymptotic optimality of the generalized cμ rule under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 206-236.

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