Abstract
In this thesis, we aim to maximize the expected utility of a risk-averse investor by allocating her wealth in a risk-free bank account, a stock, and a defaultable security. The securities' rates of return depend on a hidden continuous-time finite-state Markov chain representing the economic regime. The securities' price volatilities are determined by an observable process, which can be considered as a noisy observation of the hidden economic regime. We use a two dimensional Markov chain, with a special construction of its generator matrix, to model the joint dynamics of the hidden process and the observable process. Our model is a generalized version of the original model introduced by Capponi et al. [1]. For our generalized model, we find the dynamics of the filtered economic regime probabilities. Then, using it, we reduce the partially observed optimal control problem to a control problem with complete observation.
Committee Chair
José E. Figueroa-López
Committee Members
Nan Lin, Likai Chen
Degree
Master of Arts (AM/MA)
Author's Department
Mathematics
Document Type
Thesis
Date of Award
Spring 5-15-2020
Language
English (en)
DOI
https://doi.org/10.7936/22ms-fw42
Author's ORCID
https://orcid.org/0000-0002-7678-1072
Recommended Citation
Peng, Siqi, "Dynamic Portfolio Optimization with a Noisy Observation of the Hidden Economic Regime" (2020). Arts & Sciences Theses and Dissertations. 2045.
The definitive version is available at https://doi.org/10.7936/22ms-fw42