MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

doi:10.1016/S0252-9602(10)60175-0

Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (5): 1819-1836.doi: 10.1016/S0252-9602(10)60175-0

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MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

WU Zhen, XIAO Hua

1.School of Mathematics, Shandong University, Jinan 250100, China
2.School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, China

Received:2006-10-22 Revised:2008-11-29 Online:2010-09-20 Published:2010-09-20
Supported by:
Wu acknowledges the National Natural Science Foundation (10371067), the National Basic Research Program of China (973 Program, 2007CB814904), the Natural Science Foundation of Shandong Province (Z2006A01), the Doctoral Fund of Education Ministry of China, and Youth Growth Foundation of Shandong University at Weihai, P.R.China. Xiao acknowledges the Natural Science Foundation of Shandong Province (ZR2009AQ017), and Independent Innovation Foundation of Shandong University, IIFSDU.

Abstract

Abstract:

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result
of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

Key words: backward stochastic differential equations, comparison theorem, local time

CLC Number:

60H10

WU Zhen, XIAO Hua. MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM[J].Acta mathematica scientia,Series B, 2010, 30(5): 1819-1836.

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MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

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