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


Savku E., Weber G.

ANNALS OF OPERATIONS RESEARCH, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2020
  • Doi Number: 10.1007/s10479-020-03768-5
  • Title of Journal : ANNALS OF OPERATIONS RESEARCH
  • Keywords: Control, Stochastic processes, Behavioral finance, Game theory, Dynamic programming, MAXIMUM PRINCIPLE, ZERO-SUM, EQUATIONS, BSDES, MODEL

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 aD-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.