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 backward SDE driven by a continuous local martingale and a possibly non quasi-left-continuous random measure. Supposing that a solution (Y, Z, U ) of a backward SDE is such that Y t = v(t, X t ) where X is an underlying process and v is a deterministic function, solving the identification problem consists in determining Z and U in term of v. We study the over-mentioned identification problem under various sets of assumptions and we provide a family of examples including the case when X is a non-semimartingale jump process solution of an SDE with singular coefficients.