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Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market

Author

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  • E. Savku

    (Middle East Technical University
    École Polytechnique, CMAP)

  • G.-W Weber

    (Middle East Technical University
    Poznan University of Technology)

Abstract

We apply dynamic programming principle to discuss two optimal investment problems by using zero-sum and nonzero-sum stochastic game approaches in a continuous-time Markov regime-switching environment within the frame work of behavioral finance. We represent different states of an economy and, consequently, investors’ floating levels of psychological reactions by a D-state Markov chain. The first application is a zero-sum game between an investor and the market, and the second one formulates a nonzero-sum stochastic differential portfolio game as the sensitivity of two investors’ terminal gains. We derive regime-switching Hamilton–Jacobi–Bellman–Isaacs equations and obtain explicit optimal portfolio strategies with Feynman–Kac representations of value functions. We illustrate our results in a two-state special case and observe the impact of regime switches by comparative results.

Suggested Citation

  • E. Savku & G.-W Weber, 2022. "Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market," Annals of Operations Research, Springer, vol. 312(2), pages 1171-1196, May.
    • Handle: RePEc:spr:annopr:v:312:y:2022:i:2:d:10.1007_s10479-020-03768-5
    DOI: 10.1007/s10479-020-03768-5
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