2024/04/06 by Tian Chen, Chen, Tian, Guanxu Li +3
Decision Sciences · Economics, Econometrics and Finance · #35Q89 #49J40 #49L25 #49N80 #60J10 #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2404.07998
openalex publication_date 2024/04/06 · openalex created_date 2024/04/16 · openalex updated_date 2026/07/28
In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming principle (DPP) are established. The switching problem is characterized by an obstacle equation on the Wasserstein space, and the existence, stability, and comparison principle are obtained in the sense of viscosity solution. In particular, we consider a two-time-scale structure and obtain the convergence of the limit system. As an application of our theoretical results, an innovative example concerning the stock trading problem in a regime switching market is solved.