Stochastic Optimal Control of Conditional McKean-Vlasov Equations with Jump and Markovian Switching

Author

Charles Samuel Conly Sharp, Florida Institute of TechnologyFollow

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.

Comments

Copyright held by author.

Recommended Citation

Sharp, Charles Samuel Conly, "Stochastic Optimal Control of Conditional McKean-Vlasov Equations with Jump and Markovian Switching" (2023). Theses and Dissertations. 1380.
https://repository.fit.edu/etd/1380