A Maximum Principle for Mean-Field SDEs with time change

2016/08/21 by Di Nunno, Giulia, Haferkorn, Hannes
#60G60 #60H10 #91G80 #93E20 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1608.05993

Abstract

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.

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