Electronic Communications in Probability

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

Nicolas Saintier

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465224955

Digital Object Identifier
doi:10.1214/ECP.v12-1261

Mathematical Reviews number (MathSciNet)
MR2300220

Zentralblatt MATH identifier
1191.60090

Subjects
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

Keywords
Stochastic control jump diffusion viscosity solutions mathematical finance large investor

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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