Skew Brownian Motion with Two-Valued Drift
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：周晓文（康考迪亚大学）
：2023-04-18 08:30
：腾讯会议ID：922-560-948（无密码）
报告人：周晓文（康考迪亚大学）
时 间：2023年4月18日上午8:30-10:00
地 点：腾讯会议ID：922-560-948（无密码）
内容摘要:
We consider a skew Brownian motion with two-valued drift as the unique solution to the following SDE
\[dX_t=\big(\mu_- 1_{\{X_t<a\}}+\mu_+ 1_{\{X_t>a\}}\big)dt +dB_t+\beta dL^a_t(X),\]
where $\mu_-$ and $\mu_+ $ are constants, $-1<\beta<1$, $B$ 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 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 $\mu_-, \mu_+$ and $\beta$ affect the optimal dividend barriers. (This talk is based on joint work with Zhongqin Gao.)
个人简介：
周晓文，1999年在美国加州大学Berkeley分校获统计学博士学位。现任加拿大Concordia大学数学与统计系终身教授。长期从事概率论与随机过程理论的研究，主要研究兴趣包括测度值随机过程，勒维过程及其在种群遗传学和风险理论中的应用。先后在《Annals of Probability》、《Probability Theory and Related Fields》、《Annals of Applied Probability》等国际概率刊物发表论文60余篇。
联系人：王文元
