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

Yang Shen, Qingxin Meng, Peng Shi

Research output: Contribution to journalArticle

51 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1565-1579
Number of pages15
JournalAutomatica
Volume50
Issue number6
DOIs
Publication statusPublished - Jun 2014

Keywords

  • Backward stochastic differential equation
  • Mean-field model
  • Mean-variance portfolio selection
  • Stochastic delay differential equation
  • Stochastic maximum principle

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