Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(1): 17-28

Online first article December 21, 2016      Printed January 31, 2017

https://doi.org/10.4134/BKMS.b150007

Copyright © The Korean Mathematical Society.

Mean-field backward stochastic differential equations on Markov chains

Wen Lu and Yong Ren

Yantai University, Anhui Normal University

Abstract

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

Keywords: mean-field backward stochastic differential equations, Markov chain, comparison theorem

MSC numbers: Primary 60H20, 60H10