The maximum principles for partially observed risk-sensitive optimal controls of Markov regime-switching jump-diffusion system

This 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 exponenti...

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Bibliographic Details
Published in:Stochastic analysis and applications 2018-11, Vol.36 (5), p.782-811
Main Authors: Sun, Zhongyang, Menoukeu-Pamen, Olivier
Format: Article
Language:English
Subjects:
Convexity
Deduction
jump-diffusion
Markov analysis
Markov processes
Maximum principle
Optimal control
Optimization
Partial information
regime-switching
Risk management
risk-sensitive control
stochastic maximum principle
Switching
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Summary:This 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.
ISSN:0736-2994
1532-9356
DOI:10.1080/07362994.2018.1465824