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16-03-2024

金融数学与金融计算系列报告|Stochastic Black-Scholes equation for option pricing under a non-Markovian framework

报告人:Prof. Jinniao QiuDepartment of Mathematics and Statistics, University of Calgary, Canada

时间:2024321日周四上午1000-11:00

腾讯会议:474-989-185

报告题目:Stochastic Black-Scholes equation for option pricing under a non-Markovian framework

报告摘要:

This talks focuses on a dynamic multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and correlation matrix of the assets, and for studying the join effects on portfolio diversification. The dynamic setting allows us to consider time varying ambiguity sets, which include the cases where the drift and correlation are estimated on a rolling window of historical data or when the investor takes into account learning on the ambiguity. In this context, we prove a general separation principle for the associated robust control problem, which allows us to reduce the determination of theAbstract:

In a new paradigm of finance, the volatility exhibits roughness and path-dependence. This makes the pricing model notably non-Markovian. We shall talk about the option pricing problems with a general random volatility process. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic partial differential equation (BSPDE) or so-called stochastic Black-Scholes equation. The wellposedness of such kind of BSPDEs and associated Feynman-Kac representations will be discussed. These BSPDEs are then used to approximate American option prices. Moreover, a deep leaning-based method is also proposed and investigated for the numerical approximations to such BSPDEs and associated non-Markovian pricing problems. Two numerical examples under rough volatilities will be presented for both European and American options. This talk is mainly based on joint work with Christian Bayer and Yao Yao.

BIO:

Dr. Jinniao Qiu is an associate professor in the Department of Mathematics and Statistics, University of Calgary. He received his Ph.D. from the School of Mathematical Sciences, Fudan University, in 2012. After that, he was a postdoctoral fellow in Humboldt-University Berlin first and then a limited-term assistant professor in the University of Michigan. In 2017, he joined the University of Calgary. The research interests include stochastic control, (stochastic) PDEs, mathematical finance and economics, nonlinear dynamical systems with applications.

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