### A general stochastic target problem with jump diffusion and an application to a hedging problem for large investors

**Nicolas Saintier**

*(University of Buenos Aires)*

#### Abstract

Let $Z(t,z)$ be a $\mathbb{R}^d$-valued controlled jump diffusion starting from the point $z$ at time $t$. The aim of this paper is to characterize the set $V(t)$ of initial conditions $z$ such that $Z(t,z)$ can be driven into a given target at a given time. We do this by proving that the characteristic function of the complement $V(t)$ satisfies some partial differential equation in the viscosity sense. As an application, we study the problem of hedging in a financial market with a large investor.

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Pages: 106-119

Publication Date: April 24, 2007

DOI: 10.1214/ECP.v12-1261

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