Electronic Communications in Probability

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

Nicolas Saintier

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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.

Article information

Electron. Commun. Probab., Volume 12 (2007), paper no. 12, 106-119.

Accepted: 24 April 2007
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49J20: Optimal control problems involving partial differential equations
Secondary: 49L20: Dynamic programming method 60J60: Diffusion processes [See also 58J65] 60J75: Jump processes 35K55: Nonlinear parabolic equations

Stochastic control jump diffusion viscosity solutions mathematical finance large investor

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Saintier, Nicolas. A general stochastic target problem with jump diffusion and an application to a hedging problem for large investors. Electron. Commun. Probab. 12 (2007), paper no. 12, 106--119. doi:10.1214/ECP.v12-1261. https://projecteuclid.org/euclid.ecp/1465224955

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