Maximum principle for mean-field jump-diffusion stochastic delay differential equations and its application to finance

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• 作者：Yang Shen^a ; ^b ; ^{skyshen87@gmail.com" class="auth_mail}Author Vitae ; Qingxin Meng^c ; ^d ; ¹ ; ^{mqx@hutc.zj.cn" class="auth_mail}Author Vitae ; Peng Shi^e ; ^f ; ^{peng.shi@adelaide.edu.au" class="auth_mail}Author Vitae
• 关键词：Stochastic maximum principle ; Mean-field model ; Stochastic delay differential equation ; Backward stochastic differential equation ; Mean&ndash ; variance portfolio selection
• 刊名：Automatica
• 出版年：June 2014
• 年：2014
• 卷：50
• 期：6
• 页码：1565-1579
• 全文大小：582 K

文摘

This paper investigates a stochastic optimal control problem with delay and of mean-field type, where the controlled state process is governed by a mean-field jump–diffusion stochastic delay differential equation. Two sufficient maximum principles and one necessary maximum principle are established for the underlying system. As an application, a bicriteria mean–variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques. Under certain conditions, explicit expressions are provided for the efficient portfolio and the efficient frontier, which are as elegant as those in the classical mean–variance problem without delays.