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Portfolio Optimization Under Nonlinear Utility

Author

Listed:
  • GREGOR HEYNE

    (Department of Mathematics, Humboldt University of Berlin, Unter den Linden 6 – 10099 Berlin, Germany)

  • MICHAEL KUPPER

    (Department Mathematics and Statistics, Universität Konstanz, Universitätsstraße 10, 78464 Konstanz, Germany)

  • LUDOVIC TANGPI

    (Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria)

Abstract

This paper studies the utility maximization problem of an agent with nontrivial endowment, and whose preferences are modeled by the maximal subsolution of a backward stochastic differential equation (BSDE). We prove existence of an optimal trading strategy and relate our existence result to the existence of a maximal subsolution to a controlled decoupled forward–BSDE (FBSDE). Using BSDE duality, we show that the utility maximization problem can be seen as a robust control problem admitting a saddle point if the generator of the BSDE additionally satisfies a specific growth condition. We show by convex duality that any saddle point of the robust control problem agrees with a primal and a dual optimizer of the utility maximization problem, and can be characterized in terms of a BSDE solution.

Suggested Citation

  • Gregor Heyne & Michael Kupper & Ludovic Tangpi, 2016. "Portfolio Optimization Under Nonlinear Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:05:n:s0219024916500291
    DOI: 10.1142/S0219024916500291
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    References listed on IDEAS

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    1. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
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    Citations

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    Cited by:

    1. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
    2. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.
    3. Samuel Drapeau & Peng Luo & Dewen Xiong, 2017. "Characterization of Fully Coupled FBSDE in Terms of Portfolio Optimization," Papers 1703.02694, arXiv.org, revised Sep 2019.
    4. Olivier Menoukeu-Pamen & Ludovic Tangpi, 2023. "Maximum Principle for Stochastic Control of SDEs with Measurable Drifts," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1195-1228, June.
    5. Luo, Peng & Menoukeu-Pamen, Olivier & Tangpi, Ludovic, 2022. "Strong solutions of forward–backward stochastic differential equations with measurable coefficients," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 1-22.

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