Tingshu Mu | Searcharxiv

arXiv2022

Mean-Field Doubly Reflected Backward Stochastic Differential Equations

We study mean-field doubly reflected BSDEs. First, using the fixed point method, we show existence and uniqueness of the solution when the data which define the BSDE are $p$-integrable with $p=1$ or $p>1$. The two cases are treated separately. Next by penalization we show also the existence of the solution. The two methods do not cover the same set of assumptions.

math.PR↗

arXiv2020

Zero-sum Switching Game, Systems of Reflected Backward SDEs and Parabolic PDEs with bilateral interconnected obstacles

In this paper we study a zero-sum switching game and its verification theorems expressed in terms of either a system of Reflected Backward Stochastic Differential Equations (RBSDEs in short) with bilateral interconnected obstacles or a system of parabolic partial differential equations (PDEs in short) with bilateral interconnected obstacles as well. We show that each one of the systems has a unique solution. Then we show that the game has a value.

math.PR↗