Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information

Olivier Menoukeu Pamen ()
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Olivier Menoukeu Pamen: African Institute for Mathematical Sciences

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 2, No 5, 373-410

Abstract: Abstract This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward–backward stochastic differential equations with jumps. First, a general sufficient maximum principle for optimal control for a system, driven by a Markov regime-switching forward–backward jump–diffusion model, is developed. In the regime-switching case, it might happen that the associated Hamiltonian is not concave and hence the classical maximum principle cannot be applied. Hence, an equivalent type maximum principle is introduced and proved. In view of solving an optimal control problem when the Hamiltonian is not concave, we use a third approach based on Malliavin calculus to derive a general stochastic maximum principle. This approach also enables us to derive an explicit solution of a control problem when the concavity assumption is not satisfied. In addition, the framework we propose allows us to apply our results to solve a recursive utility maximization problem.

Keywords: Forward–backward stochastic differential equations; Malliavin calculus; Regime switching; Recursive utility maximization; Stochastic maximum principle; 93E30; 91G80; 91G10; 60G51; 60HXX; 91B30 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-017-1144-x

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