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Continuity of utility maximization under weak convergence

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, USA

    Erhan Bayraktar

  2. Department of Statistics, Hebrew University, Jerusalem, Israel

    Yan Dolinsky

  3. Department of Mathematics, University of Michigan, Ann Arbor, USA

    Jia Guo

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  1. Erhan Bayraktar
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  2. Yan Dolinsky
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  3. Jia Guo
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Correspondence to Erhan Bayraktar.

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E. Bayraktar is supported in part by the National Science Foundation and in part by the Susan M. Smith Professorship. Y. Dolinsky is supported in part by the Israeli Science Foundation under Grant 160/17.

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Bayraktar, E., Dolinsky, Y. & Guo, J. Continuity of utility maximization under weak convergence. Math Finan Econ 14, 725–757 (2020). https://doi.org/10.1007/s11579-020-00274-x

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