Risk Minimizing Portfolio Optimization and Hedging with Conditional Value-at-Risk

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Li, J. (2009). Risk Minimizing Portfolio Optimization and Hedging with Conditional Value-at-Risk. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

This thesis looks at the problem of finding the optimal investment strategy of a self-financing portfolio in a dynamic complete market setting so that the risk measured by Conditional Value-at-Risk (CVaR) is minimized under the condition that the expected return is bounded from below.We start out with a CVaR minimization problem without expected return requirement. We find the exact optimal conditions and apply them to two classic complete market models: the Binomial model and the Black-Scholes model. In these cases, the procedures of finding the optimal strategies are given with exact formulas, and the resulting minimal CVaR values can be calculated.We then add a minimal expected return constraint, and look for an optimal solution in a continuous-time setting. The optimal solution most likely does not exist if there is no upper bound on returns over time, but the infimum of CVaR can still be computed. However, when such a uniform upper bound is prescribed, we find the optimal conditions together with the optimal investment strategy and the resulting minimal CVaR.

Details
Author

Li, Jing

Title

Risk Minimizing Portfolio Optimization and Hedging with Conditional Value-at-Risk

Physical Description

1 online resource (86 pages) : PDF

Date

2009

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

This thesis looks at the problem of finding the optimal investment strategy of a self-financing portfolio in a dynamic complete market setting so that the risk measured by Conditional Value-at-Risk (CVaR) is minimized under the condition that the expected return is bounded from below.We start out with a CVaR minimization problem without expected return requirement. We find the exact optimal conditions and apply them to two classic complete market models: the Binomial model and the Black-Scholes model. In these cases, the procedures of finding the optimal strategies are given with exact formulas, and the resulting minimal CVaR values can be calculated.We then add a minimal expected return constraint, and look for an optimal solution in a continuous-time setting. The optimal solution most likely does not exist if there is no upper bound on returns over time, but the infimum of CVaR can still be computed. However, when such a uniform upper bound is prescribed, we find the optimal conditions together with the optimal investment strategy and the resulting minimal CVaR.

Genre

doctoral dissertations

Subjects--Topics

Mathematics

Degree

Ph.D.

Keywords

Coherent Risk Measure
Conditional Value-At-Risk
Convex Duality
Portfolio Optimization and Hedging
Portfolio Selection
Risk Minimization

Subject Area

Applied Mathematics

Advisor(s)

Xu, Mingxin

Committee Members

Wihstutz, Volker
Zhu, You-lan
Shapiro, Dmitry

Degree Note

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2009.

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Rights Holder Information

Copyright is held by the author unless otherwise indicated.

Identifier

Li_uncc_0694D_10021

Permalink

http://hdl.handle.net/20.500.13093/etd:1311