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5 results on '"Mu, Tingshu"'

1. Mean-Field Doubly Reflected Backward Stochastic Differential Equations

Author

Chen, Yinggu, Hamadene, Said, and Mu, Tingshu

Subjects
Mathematics - Probability, 49N80, 91A16, 91G66
Abstract

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., Comment: 22 pages

Published
2020

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

Author

Hamadène, Said and Mu, Tingshu

Subjects
Mathematics - Probability
Abstract

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.

Published
2020

5. Systems of reflected BSDEs with interconnected bilateral obstalces: Existence, Uniqueness and Applications

Author

Hamadène, Said, Mu, Tingshu, Laboratoire Manceau de Mathématiques (LMM), Le Mans Université (UM), Laboratoire de modélisation en mécanique (LMM), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Zero-sum stochastic switching games, Viscosity solution, Optimal switching, Systems of reflected BSDEs, Bilateral interconnected obstacles, Feynman-Kac representation, Systems of PDEs with interconnected obstacles
Abstract

This paper is related to the study of systems of reflected backward stochastic differential equations with interconnected bilateral obstacles. These systems are connected with zero-sum stochastic switching games. Under appropriate assumptions, we provide either existence or existence and uniqueness of the solution of those systems when the switching costs are Itô processes. The link with systems of PDEs with bilateral interconnected obstacles is also stated via the Feynman-Kac representation when randomness comes from a Markov diffusion process. AMS Classification subjects: 93C30 ; 91A15 ; 93E20 ; 49J20.

Published
2019

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