青年教师学术论坛（数学）第七期预告

时间：2014年5月15日（周四） 下午3:30

地点：浦江办公楼408会议室

内容： Adapted Solution, Numerical Methods and Analysis via Malliavin Calculus for A United B-SPDE and Applications in Finance and IT Technology

主讲人：南京大学 戴万阳 教授

Abstract

This research is to study the adapted solution, numerical methods, and related convergence analysis for a united backward stochastic partial differential equation (B-SPDE). The equation is vector-valued, whose drift and diffusion coefficients may involve non-linear and high-order partial differential operators. Under certain generalized Lipschitz and linear growth conditions, the existence and uniqueness of adapted solution to the B-SPDE are justified. The methods are based on completely discrete schemes in terms of both time and space. The analysis concerning error estimation or rate of convergence of the methods is conducted. The key of the analysis is to develop new theory for random field based Malliavin calculus to prove the existence and uniqueness of adapted solutions to the ¯rst-order and second-order Malliavin derivative based B-SPDEs under random environments. Furthermore, we will also address the related issues of our united B-SPDE involving jumps and long-range dependence. In addition, we will present the applications of our united B-SPDE in several areas including finance, Dirichlet-Poisson Problem, optimal control, statistical physics and quantum mechanics. In particular, we will discuss the application of the equation in the fields of optimal portfolio decision-making and

mean-variance hedging with external random environmental risk factors.

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