报告题目：Optimal Dividend Problem for a Risk Process with Endogenous Regime Switching

报告时间：2024.11.20  21：00-22：00

报告地点：腾讯会议782-957-226

报告人简介：周晓文教授，1988年本科毕业于中山大学，1999年在加州大学Berkeley 分校 获得统计学博士学位。现为加拿大Concordia大学终身教授。主要研究领域是随机过程及其应用。共发表90余篇学术论文。

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

dXt = µ−1{Xt<a} + µ+1{Xt>a} dt + dBt + βdLa t (X),

where µ− and µ+ are constants, −1 < β < 1, B is a Brownian motion and L a t (X) 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 threshold level a.

In this talk we find Laplace transforms of exit times for the skew Brownian motion, and consider an optimal control problem in which we look for an optimal dividend strategy that maximizes the expected accumulated present value of dividends until ruin for the skew Brownian risk process for insurance. We identify conditions for different barrier strategies to be optimal and observe that certain band strategies involving two dividend barriers can also be optimal.

This talk is based on joint work with Zhongqin Gao and Yan Lv.