Solvability of general backward stochastic Volterra integral equation with non-Lipschitz coefficients

2010/01/20 by Tianxiao Wang, Wang, Tianxiao, Yufeng Shi +1
Mathematics · #49K22 #60H20 #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR) #math.GR #math.PR #msc:49K22 #msc:60H20

paper · pdf · doi:10.48550/arxiv.1001.3557

arxiv created 2010/01/20 · arxiv updated 2010/02/26

Abstract

In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the M-solutions introduced in [17] and the adapted solutions in [6], [12] or [14]. A general existence and uniqueness of M-solutions is proved under non-Lipschitz conditions by virtue of a briefer argument than the one in [17], which also extends the results in [17]. For the adapted solutions, the unique solvability of BSVIEs, under more general stochastic non-Lipschitz conditions, is obtained which generalizes the results in [6], [12] and [14].

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