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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/11248

Title: Asymptotic Optimization of Risk Measures
Authors: Quintanilla, Maria Teresa
Advisor: Sulem, Catherine
Department: Mathematics
Keywords: optimization
Issue Date: 1-Aug-2008
Abstract: Value-at-Risk (VaR ) is an industrial standard for monitoring market risk in an investment portfolio. It measures potential osses within a given confidence level. VaR was first used by major financial institutions in the early 1990’s, and widely developed after the release of J.P. Morgan’s Riskmetrics Technical Document in 1996. The efficient calculation, implementation, interpretation and optimization of VaR are a challenge in the practice of risk management when the number of market factors in the portfolio is high. In this thesis, we are concerned with the quadratic analytical estimation of VaR and we present a methodology for an approximation to VaR that is based on the principal components of a sensitivity-adjusted covariance matrix. The result is an explicit expression in terms of portfolio deltas, gammas, and the mean and covariance matrix. It can be viewed as a non-linear extension of the linear model given by the delta-normal-VaR of RiskMetrics, a standard calculation for the risk in the financial sector. We obtain an asymptotic expansion for VaR in the limit when the confidence level approaches 1 and precise estimates of the reminder. We then optimize the approximated VaR with respect to the gradient or delta of the portfolio, a quantity which can be changed by trading the underlying assets (stocks), without entering into any derivative transactions. This analysis provides an optimal trading strategy of the portfolio that minimizes the risk.
URI: http://hdl.handle.net/1807/11248
Appears in Collections:Doctoral
Department of Mathematics - Doctoral theses

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