Articlebronze1985

Reflected Diffusion Processes with Jumps

60 citations0/0 files storedThe Annals of Probability

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Stochastic processes and statistical mechanics

Abstract

A stochastic differential equation of Wiener-Poisson type is considered in a $d$-dimensional bounded region. By using a penalization argument on the domain, we are able to prove the existence and uniqueness of solutions in the strong sense. The main assumptions are Lipschitzian coefficients, either convex or smooth domains and a regular outward reflecting direction. As a direct consequence, it is verified that the reflected diffusion process with jumps depends on the initial date in a Lipschitz fashion.

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2004Optimal Control Problem Associated with Jump Processes 2008Stochastic PDIEs with nonlinear Neumann boundary conditions and generalized backward doubly stochastic differential equations driven by Lévy processes 2010Optimal portfolios of a small investor in a limit order market: a shadow price approach 2009Ergodic BSDEs and related PDEs with Neumann boundary conditions 2003Penalization methods for reflecting stochastic differential equations with jumps 1992Singular ergodic control for multidimensional Gaussian processes 2006Generalized BSDE driven by a Lévy process 2012Weak and strong approximations of reflected diffusions via penalization methods

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