Backward stochastic differential equation with local time

Abstract

In this paper we deal with the following backward stochastic differential equation:

where W is a d-dimensional Brownian motion is the symmetric local time of Fat the level a, v is a signed measure on is a -measurable random variable in and is an adapted map from to .

If h is continuous with linear growth, we show the existence of a solution (Y,Z) for this backward equation. Some applications of this result, in connection with partial differential equations, and with linear quadratic stochastic control problem, are also given

Keywords:

• Backward stochastic differential equation
• local time
• AMS Subject Classifications: 60H15, 60H30

Notes

^*Corresponding author

Additional information

Notes on contributors

A. Dermoune

^*

S. Hamadéne