# American Institute of Mathematical Sciences

December  2017, 7(4): 585-622. doi: 10.3934/mcrf.2017022

## Time-inconsistent optimal control problems with regime-switching

 School of Statistics, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China

Received  January 2016 Revised  April 2017 Published  September 2017

In this paper, a time-inconsistent optimal control problem is studied for diffusion processes modulated by a continuous-time Markov chain. In the performance functional, the running cost and terminal cost depend on not only the initial time, but also the initial state of the Markov chain. By modifying the method of multi-person game, we obtain an equilibrium Hamilton-Jacobi-Bellman equation under proper conditions. The well-posedness of this equilibrium HJB Equation is studied in the case where the diffusion term is independent of the control variable. Furthermore, a time-inconsistent linear-quadratic control problem is considered as a special case.

Citation: Jiaqin Wei. Time-inconsistent optimal control problems with regime-switching. Mathematical Control & Related Fields, 2017, 7 (4) : 585-622. doi: 10.3934/mcrf.2017022
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The solutions for $P(1,t,1)$ and $P(2,t,2)$

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