期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 267, 期 -, 页码 1-19出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2014.01.021
关键词
Stochastic optimal control; Jump-diffusion; Markov-switching; Optimal consumption-investment
资金
- FCT-Fundacao para a Ciencia e a Tecnologia [SFRH-BD-67186-2009]
- CEMAPRE
- FCT-Fundacao para a Ciencia e a Tecnologia through the Program POCI
- Fundação para a Ciência e a Tecnologia [SFRH/BD/67186/2009] Funding Source: FCT
We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Levy process and the Markov process. As an application of our results, we study a finite horizon consumption-investment problem for a jump-diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities. (C) 2014 Elsevier B.V. All rights reserved.
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