SOLVABILITY OF GENERAL BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS

- Journal title : Journal of the Korean Mathematical Society
- Volume 49, Issue 6, 2012, pp.1301-1321
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2012.49.6.1301

Title & Authors

SOLVABILITY OF GENERAL BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS

Shi, Yufeng; Wang, Tianxiao;

Shi, Yufeng; Wang, Tianxiao;

Abstract

In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the adapted M-solutions introduced in [19] and the adapted solutions via a new method. A general existence and uniqueness of adapted M-solutions is proved under non-Lipschitz conditions by virtue of a briefer argument than the ones in [13] and [19], which modifies and extends the results in [13] and [19] respectively. For the adapted solutions, the unique solvability of BSVIEs under more general stochastic non-Lipschitz conditions is shown, which improves and generalizes the results in [7], [14] and [15].

Keywords

backward stochastic Volterra integral equations;adapted solutions;adapted M-solutions;non-Lipschitz conditions;stochastic Lipschitz coefficients;

Language

English

Cited by

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