Numerical Solutions to Stochastic Model and Their Applications

Dear Colleagues,

For decades, stochastic modeling has been widely applied in fields such as economics, finance, insurance, population dynamics, epidemiology, and engineering. The stochastic differential equation (SDE), random algorithm, and stochastic optimal control play central roles in solving various modeling and decision-making problems.  For example,  SDEs provide the essential stochastic modeling device for modern financial theory and sampling algorithms in machine learning. In addition, most of the practical problems in finance and insurance are stochastic optimal control problems, in which optimal decisions (controls) are made based on information from the underlying dynamics over time. Such problems can be tackled with dynamic programming and Hamilton–Jacobi‒Bellman (HJB) equations or backward stochastic differential equations (BSDEs). However, for most of the applications, the underlying dynamics are so complex that the associated (B)SDEs or HJB equations cannot be analytically solved, thus necessitating the use of numerical methods for finding their approximated solutions. In machine learning and statistics, efficient algorithms usually rely heavily on fast sampling schemes, which account for most of the running times. 

This Special Issue is devoted to collect contributions in numerical methods, random algorithms, and solutions of stochastic modeling and their applications. The topics include numerical solutions for various SDEs and BSDEs and their applications in finance and insurance, numerical solutions for stochastic optimal control problems, deep learning and reinforcement learning algorithms for BSDEs, optimal control, optimal stopping problems, etc.

Prof. Dr. Conghua Wen
Dr. Youzhou Zhou
Dr. Ran Xu
Prof. Dr. Zhuo Jin
Guest Editors

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