The identification problem for BSDEs driven by possibly non-quasi-left-continuous random measures

Abstract

In this paper, we focus on the so-called identification problem for a BSDE driven by a continuous local martingale and a possibly non-quasi-left-continuous random measure. Supposing that a solution [Formula: see text] of a BSDE is such that [Formula: see text] where [Formula: see text] is an underlying process and [Formula: see text] is a deterministic function, solving the identification problem consists in determining [Formula: see text] and [Formula: see text] in terms of [Formula: see text]. We study the over-mentioned identification problem under various sets of assumptions and we provide a family of examples including the case when [Formula: see text] is a non-semimartingale jump process solution of an SDE with singular coefficients.