A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications

Olivier Menoukeu-Pamen () and Romuald Hervé Momeya ()
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Olivier Menoukeu-Pamen: African Institute for Mathematical Sciences Ghana
Romuald Hervé Momeya: CIBC Asset Management Inc.

Mathematical Methods of Operations Research, 2017, vol. 85, issue 3, No 2, 349-388

Abstract: Abstract In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward–backward stochastic differential equations with jumps. First, we prove a sufficient maximum principle for nonzero-sum stochastic differential games problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for nonzero-sum stochastic differential games. The zero-sum stochastic differential games equivalent maximum principle is then obtained as a corollary. We apply the obtained results to study a problem of robust utility maximization under a relative entropy penalty and to find optimal investment of an insurance firm under model uncertainty.

Keywords: Forward–backward stochastic differential equations; Markov regime-switching; Stochastic differential games; Optimal investment; Stochastic maximum principle; IM00; IM50; 93E30; 91G80; 91G10; 60G51; 60HXX; 91B30 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-017-0574-4

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