Date of Award

12-2023

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Systems Engineering

First Advisor

Son Luu Nguyen

Second Advisor

Kim-Doang Nguyen

Third Advisor

Ryan White

Fourth Advisor

Gnana Bhaskar Tenali

Abstract

This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.

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