Non-explosion and pathwise uniqueness of strong solutions for jump-type stochastic differential equations driven by optional semimartingales under non-Lipschitz conditions

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 (làdlàg) 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.