Abstract

We consider a skew Brownian motion with two-valued drift as the unique solution to the following SDE

where  and are constants, , B is a Brownian motion and denotes the symmetric local time for X at level a. Such a process can be identified as a toy model for regime switching that depends on whether the process $X$ takes values above or below the level $a$.

In this talk we first solve the exit problems for the skew Brownian motion. Inspired by the dividend problem for risk processes, we further study the optimal dividend problem for such models and discuss how the parameters  and affect the optimal dividend strategies.

This talk is based on joint work with Zhongqin Gao.