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Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market
Date
2020-08-01
Author
Savku, E.
Weber, Gerhard Wilhelm
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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.
Subject Keywords
Management Science and Operations Research
,
General Decision Sciences
URI
https://hdl.handle.net/11511/51595
Journal
ANNALS OF OPERATIONS RESEARCH
DOI
https://doi.org/10.1007/s10479-020-03768-5
Collections
Graduate School of Applied Mathematics, Article
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BibTeX
E. Savku and G. W. Weber, “Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market,”
ANNALS OF OPERATIONS RESEARCH
, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51595.