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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 41, Fasc. 2,
pages 193 - 215
DOI: 10.37190/0208-4147.41.2.1
Published online 19.8.2021
 

A time-changed stochastic control problem and its maximum principle maximum principle

Erkan Nane
Yinan Ni

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 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.

2010 AMS Mathematics Subject Classification: Primary 93E20, 39A50, 60H05;

Keywords and phrases: optimal stochastic control, time-changed L\'evy process, maximum principle

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