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A risk-sensitive maximum principle for a Markov regime-switching jump-diffusion system and applications
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 985-1013

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In this paper, we derive a general stochastic maximum principle for a risk-sensitive type optimal control problem of Markov regime-switching jump-diffusion model. The results are obtained via a logarithmic transformation and the relationship between adjoint variables and the value function. We apply the results to study both a linear-quadratic optimal control problem and a risk-sensitive benchmarked asset management problem for Markov regime-switching models. In the latter case, the optimal control is of feedback form and is given in terms of solutions to a Markov regime-switching Riccatti equation and an ordinary Markov regime-switching differential equation.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017039
Classification : 93E20, 91G80
Keywords: Risk-sensitive control, Regime-switching, Jump-diffusion, Stochastic maximum principle, Asset management

Sun, Zhongyang 1 ; Kemajou-Brown, Isabelle 1 ; Menoukeu-Pamen, Olivier 1

1 
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     title = {A risk-sensitive maximum principle for a {Markov} regime-switching jump-diffusion system and applications},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {985--1013},
     publisher = {EDP-Sciences},
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Sun, Zhongyang; Kemajou-Brown, Isabelle; Menoukeu-Pamen, Olivier. A risk-sensitive maximum principle for a Markov regime-switching jump-diffusion system and applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 985-1013. doi: 10.1051/cocv/2017039

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