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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.
This paper considers a forward BSDE driven by a random measure, when the underlying forward process X is special semimartingale, or even more generally, a special weak Dirichlet process. Given a solution (Y, Z, U), generally Y appears to be of the ty
The paper analyzes risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for bounded cd
In this paper, we consider a reflected backward stochastic differential equation driven by a $G$-Brownian motion ($G$-BSDE), with the generator growing quadratically in the second unknown. We obtain the existence by the penalty method, and a priori e
In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion (RGBSDE for short). The reflection keeps the solution above a given stochastic process. In order to derive the u
In this paper, we will prove that, if the coefficient $g=g(t,y,z)$ of a BSDE is assumed to be continuous and linear growth in $(y,z)$, then the uniqueness of solution and continuous dependence with respect to $g$ and the terminal value $xi$ are equivalent.