Speaker：Zhen Wu (Shandong University)

Time：2019-01-11,17:00

Location：Conference Room B313 at Administration Building at Haiyun Campus

Abstract: This talk is concerned with backward stochastic differential equations (BSDEs) optimal switching problem coupled by  continuous-time finite-state Markov chain which has a two-time-scale structure, i.e., the states of the Markov chain can be divided into a number of groups such that the chain jumps rapidly within a group slowly between the groups. In this talk, we give some convergence results as the fast jump rate goes to infinity, which can be used to reduce the complexity of the original problem. This method is also referred to as singular perturbation. The first result is the weak convergence of the BSDEs with two-time-scale Markov chains. It is shown that the solution of the original BSDE system converges weakly under the Meyer-Zheng topology to that of an aggregated BSDE system. Then we focus on the optimal switching problem for regime switching model with two-time-scale Markov chains. We obtain the optimal switching strategy by virtue of dynamic programming principle related HJB equation—a system of variational  inequality，prove the convergence of the value function under the two-time-scale structure. Finally, as an  application of the theoretical results, an example concerning the stock trading problem in a regime switching market is provided. Both the optimal trading rule convergence result are numerically demonstrated in this example.