BSDEs with regime switching: Weak convergence and applications

作者：Tao Ran; Wu Zhen^*; Zhang Qing

来源：Journal of Mathematical Analysis and Applications, 2013, 407(1): 97-111.

DOI：10.1016/j.jmaa.2013.05.011

• Backward stochastic differential equations
• Markov chains
• Singular perturbation
• Weak convergence
• Meyer-Zheng topology
• Partial differential equation systems

This paper is concerned with a system of backward stochastic differential equations (BSDEs) with regime switching. The BSDEs are coupled by a finite-state Markov chain. The underlying Markov chain is assumed to have a two-time scale (or weak and strong interactions) structure. Namely, the states of the Markov chain can be divided into a number of groups so that the chain jumps rapidly within a group and slowly between the groups. It is shown in this paper that the original BSDE system can be approximated by a limit system in which the states in each group are aggregated out and replaced by a single state. In particular, it is proved that the solution of the original BSDE system converges weakly under the Meyer-Zheng topology as the fast jump rate goes to infinity. The limit process is a solution of aggregated BSDEs which can be determined by the corresponding martingale problem. The results are applied to a set of partial differential equations and used to validate their convergence to the corresponding limit system. Finally, a numerical example is given to demonstrate the approximation results.

• 出版日期2013-11-1
• 单位山东大学