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

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

2010-01-20

arxiv.org/abs/1001.3557v1

Mathematics

Probability

Scientific paper

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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