Time-changed Stochastic Control Problem and its Maximum Principle Theory

2019/05/28 by Nane, Erkan, Ni, Yinan
#65C30 #93E20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1905.11921

Abstract

This paper studies a time-changed stochastic control problem, where the underlying stochastic process is a Lévy noise time-changed by an inverse subordinator. We establish a maximum principle theory for the time-changed stochastic control problem. We also prove the existence and uniqueness of the corresponding time-changed backward stochastic differential equation involved in the stochastic control problem. Some examples are provided for illustration.

Related

• BSDEs driven by time-changed Lévy noises and optimal control
• A Maximum Principle for Mean-Field SDEs with time change
• Stochastic Volterra equations with time-changed Lévy noise and maximum principles
• Time-Reversal of Stochastic Maximum Principle
• Maximum principles for stochastic time-changed Volterra games