Volume 24, Number 3, July–September 2018
|Page(s)||985 - 1013|
|Published online||07 June 2018|
A risk-sensitive maximum principle for a Markov regime-switching jump-diffusion system and applications
School of Mathematics, Sun Yat-sen University,
510275, People’s Republic of China
2 Actuarial Science Program, Department of Mathematics, Morgan State University, Maryland 21251, USA
3 African Institute for Mathematical Sciences, University of Ghana, Ghana
4 Institute for Financial and Actuarial Mathematics, Department of Mathematics, University of Liverpool, L69 7ZL, United Kingdom
a Corresponding author: email@example.com
Revised: 8 March 2017
Accepted: 21 May 2017
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.
Mathematics Subject Classification: 93E20 / 91G80
Key words: Risk-sensitive control / Regime-switching / Jump-diffusion / Stochastic maximum principle / Asset management
© EDP Sciences, SMAI 2018
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