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Mathematics Colloquium

Friday, 04 April, 2014

SPEAKER:  Prof. Zen Wu, Shandong University

HOST:  Prof. Jie Xiong

TITLE: BSDEs with two-time-scale Markov chains and applications

ABSTRACT: This talk is concerned with with backward stochastic differential equations (BSDEs) coupled by a finite-state Markov chains. This kind of BSDEs have wide applications in optimal control and mathematical finance. The underlying Markov chain is assumed to have a two-time scale 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. In this talk, we consider two 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 one is the weak convergence of the BSDEs with two-time-scale BSDEs. It is proved that the solution of the original BSDE system converges weakly under the Meyer-Zheng topology. The limit process is a solution  of aggregated BSDEs. The results are applied to a set of partial differential equations and used to validate their convergence to the corresponding limit system.

The second one is the optimal switching problem for regime-switching model with two-time-scale Markov chains. We use a probabilistic approach to solve the problem. To be specific, we obtain the optimal switching strategy by virtue of the oblique reflected BSDEs with Markov chains. Under the two-time-scale structure, we prove the convergence of the variational inequalities.

Numerical examples are given for both of the problems to demonstrate the approximation results.

Refreshments will be available at 3:10 p.m.




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