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

E. Savku () and Weber G.-W
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E. Savku: Middle East Technical University
Weber G.-W: Middle East Technical University

Annals of Operations Research, 2022, vol. 312, issue 2, No 21, 1196 pages

Abstract: 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.

Keywords: Control; Stochastic processes; Behavioral finance; Game theory; Dynamic programming (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10479-020-03768-5

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