NON-EXPLOSION AND PATHWISE UNIQUENESS OF STRONG SOLUTIONS FOR JUMP-TYPE STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY OPTIONAL SEMIMARTINGALES UNDER NON-LIPSCHITZ CONDITIONS

NON-EXPLOSION AND PATHWISE UNIQUENESS OF STRONG SOLUTIONS FOR JUMP-TYPE STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY OPTIONAL SEMIMARTINGALES UNDER NON-LIPSCHITZ CONDITIONS

M. Haddadi, K. Akdim

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Abstract

This paper is devoted to the question of the pathwise uniqueness and the non-explosion property of strong solutions for a class of jump-type stochastic differential equations (JSDEs) with respect to optional semimartingales under non-Lipschitz conditions. Optional semimartingales have right and left limits (l`adl`ag) but are not necessarily continuous, therefore, defined on unusual probability spaces. Some models in financial and insurance mathematics which can be described by the jump-type stochastic differential equations (JSDEs) are presented.

Keywords

jump-type stochastic differential equation; optional semimartingale; Nonexplosive solution; Non-Lipschitz condition.