Optimal control of mean-field jump-diffusion systems with delay: a stochastic maximum principle approach

• Qingxin Meng ^[1] ; Yang Shen ^[2]
  1. [1] Huzhou University

     Huzhou University

     China

     
  2. [2] The University of New South Wales (Australia)
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 279, Nº 1 ((1 May 2015)), 2015, págs. 13-30
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.10.011
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• Resumen

  • This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles.