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http://hdl.handle.net/11375/14127
Title: | Portfolio Optimization under Value at Risk, Average Value at Risk and Limited Expected Loss Constraints |
Authors: | Gambrah, Priscilla S.N |
Advisor: | Pirvu, Traian A David Lozinski, Tom Hurd |
Department: | Mathematics and Statistics |
Keywords: | Portfolio Optimization;Average Value at Risk;Risk Management;Value at Risk;Geometric Brownian Motion;Mean-Reverting Model;Finance and Financial Management;Other Applied Mathematics;Portfolio and Security Analysis;Finance and Financial Management |
Publication Date: | 2014 |
Abstract: | <p>In this thesis we investigate portfolio optimization under Value at Risk, Average Value at Risk and Limited expected loss constraints in a framework, where stocks follow a geometric Brownian motion. We solve the problem of minimizing Value at Risk and Average Value at Risk, and the problem of finding maximal expected wealth with Value at Risk, Average Value at Risk, Limited expected loss and Variance constraints. Furthermore, in a model where the stocks follow an exponential Ornstein-Uhlenbeck process, we examine portfolio selection under Value at Risk and Average Value at Risk constraints. In both geometric Brownian motion (GBM) and exponential Ornstein-Uhlenbeck (O.U) models, the risk-reward criterion is employed and the optimal strategy is found. Secondly, the Value at Risk, Average Value at Risk and Variance is minimized subject to an expected return constraint. By running numerical experiments we illustrate the effect of Value at Risk, Average Value at Risk, Limited expected loss and Variance on the optimal portfolios. Furthermore, in the exponential O.U model we study the effect of mean-reversion on the optimal strategies. Lastly we compare the leverage in a portfolio where the stocks follow a GBM model to that of a portfolio where the stocks follow the exponential O.U model.</p> |
URI: | http://hdl.handle.net/11375/14127 |
Identifier: | opendissertations/8956 10034 5537594 |
Appears in Collections: | Open Access Dissertations and Theses |
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fulltext.pdf | 1.09 MB | Adobe PDF | View/Open |
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