The maximum principle for a jump-diffusion mean-field model and its application to the mean-variance problem

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• 作者：Yang Shen^a ; ^{skyshen87@gmail.com} ; Tak Kuen Siu^b ; ^a ; ^{ktksiu2005@gmail.com}
• 关键词：Mean-field model ; Stochastic maximum principle ; Jump-diffusion ; Backward stochastic differential equation ; Mean&ndash ; variance portfolio selection
• 刊名：Nonlinear Analysis
• 出版年：2013
• 出版时间：July, 2013
• 年：2013
• 卷：86
• 期：Complete
• 页码：58-73
• 全文大小：450 K

文摘

This paper establishes a necessary and sufficient stochastic maximum principle for a mean-field model with randomness described by Brownian motions and Poisson jumps. We also prove the existence and uniqueness of the solution to a jump-diffusion mean-field backward stochastic differential equation. A new version of the sufficient stochastic maximum principle, which only requires the terminal cost is convex in an expected sense, is applied to solve a bicriteria mean-variance portfolio selection problem.