Type
Text
Type
Dissertation
Advisor
Rachev, Svetlozar
Date
2015-08-01
Keywords
Mathematics
Department
Department of Applied Mathematics and Statistics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76349
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Quantifying the risk of the uncertainty in the future value of a portfolio is a key task in risk management. For decades many researchers have been trying to formalize sophisticated risk measures and apply them in the real financial world. In view of that this dissertation is dedicated to investigate the development of risk measures along with the applications in risk management, particularly in partial hedging under stochastic interest rate. In this dissertation we assess the partial hedging problems by formulating hedging strategies that minimize conditional value-at-risk (CVaR) of the portfolio loss under stochastic interest rate environment. The combination of stochastic interest and CVaR hedging method makes the valuing approach more complex than the existing model with constant interest rate. We take up two issues in searching the optimal CVaR hedging strategy: given the initial capital constraint we minimize the CVaR of the portfolio loss; by prescribing a bound on the risk, we also minimize the hedging cost. As an illustration of this hedging technique we derive hedging strategies for a European call option with the Black Scholes setting under HJM framework; explicit formulas are presented. We also investigate CVaR hedging problems by using the real financial data. The last chapter in this dissertation investigate nominal and robust portfolio optimization by employing difference version of CVaR as the risk measure. We assume that the return only known to follow a distribution set. High frequency data is used to test the performance of CVaR optimization and Worst CVaR optimization with contrast to a equally weighted portfolio. | 102 pages
Recommended Citation
Tsao, Angela, "Monetary Risk Measure with Applications in Portfolio Management-Partial Hedging" (2015). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2273.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2273