主题：Skew Brownian Motion with Two-Valued Drift and its Applications in Optimal Control
主讲人：周晓文 Concordia University
主持人：柳向东 太阳城集团
时间：2023年6月1日（周四）上午10：00-11：30
地点：太阳城集团石牌校区tyc1286太阳成集团大楼（中惠楼）102室
摘要
Motivated by its applications in the optimal dividend problem in actuarial science, we consider a skew Brownian motion with two-valued drift as the unique solution to stochastic differential equation.
Driven by Brownian motion and symmetric local time process at level with drift coefficients and and skewness . Such a process can be identified as a toy model for spatial regime switching.
In this talk we first apply the Ito-Tanaka-Meyer formula together with a martingale approach to find Laplace transforms of exit times for the skew Brownian motion.
We further 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 surplus process. By showing a verification theorem on the associated Hamilton-Jacobi-Bellman inequalities, we identify conditions for different barrier strategies to be optimal and observe that certain band strategies involving two dividend barriers can be optimal. We also illustrate how the optimal strategies are affected by different choices of drifts and skewness.
This talk is based on joint work with Zhongqin Gao.
主讲人简介
Xiaowen Zhou received BSc in mathematics from Sun Yat-Sen University and PhD in statistics from University of California at Berkeley. He joined Concordia University in 2001. His research interest is on stochastic processes and their applications in population models and in risk theory.
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校对|王国长
编辑|麦嘉杰
初审|黄振
终审|郑贤
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