A Maximum Principle for Mean-Field SDEs with Time Change

作者：Di Nunno Giulia^*; Haferkorn Hannes

来源：Applied Mathematics and Optimization, 2017, 76(1): 137-176.

DOI：10.1007/s00245-017-9426-0

• Time change
• Martingale random fields
• Mean-field SDE
• Mean-field BSDEs
• Mean-field stochastic optimal control

Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field stochastic differential equation. We consider a mean-field stochastic control problem for mean-field controlled dynamics and we present a necessary and a sufficient maximum principle. For this we study existence and uniqueness of solutions to mean-field backward stochastic differential equations in the context of time change. An example of a centralised control in an economy with specialised sectors is provided.

• 出版日期2017-8