2017/12/27 by Hongwei Mei, Mei, Hongwei, Jiongmin Yong +1
Decision Sciences · Economics, Econometrics and Finance · #Climate Change Policy and Economics #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1712.09505
openalex publication_date 2017/12/27 · openalex created_date 2018/01/05 · openalex updated_date 2026/07/28
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is time-inconsistent in general. Therefore, instead of finding a global optimal control (which is not possible), we look for a time-consistent (approximately) locally optimal equilibrium strategy. Such a strategy can be represented through the solution to a system of partial differential equations, called an equilibrium Hamilton-Jacob-Bellman (HJB, for short) equation which is constructed via a sequence of multi-person differential games. A verification theorem is proved and, under proper conditions, the well-posedness of the equilibrium HJB equation is established as well.