The maximum principles for partially observed risk-sensitive optimal controls of Markov regime-switching jump-diffusion system |
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Authors: | Zhongyang Sun |
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Institution: | School of Mathematics, Sun Yat-sen University, Guangzhou, People's Republic of China |
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Abstract: | ABSTRACTThis paper studies partially observed risk-sensitive optimal control problems with correlated noises between the system and the observation. It is assumed that the state process is governed by a continuous-time Markov regime-switching jump-diffusion process and the cost functional is of an exponential-of-integral type. By virtue of a classical spike variational approach, we obtain two general maximum principles for the aforementioned problems. Moreover, under certain convexity assumptions on both the control domain and the Hamiltonian, we give a sufficient condition for the optimality. For illustration, a linear-quadratic risk-sensitive control problem is proposed and solved using the main results. As a natural deduction, a fully observed risk-sensitive maximum principle is also obtained and applied to study a risk-sensitive portfolio optimization problem. Closed-form expressions for both the optimal portfolio and the corresponding optimal cost functional are obtained. |
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Keywords: | Partial information risk-sensitive control regime-switching jump-diffusion stochastic maximum principle |
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