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J. Risk Financial Manag. 2014, 7(3), 113-129; doi:10.3390/jrfm7030113

Risk Measures and Portfolio Optimization

Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4L8, Canada
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Received: 14 July 2014 / Revised: 28 August 2014 / Accepted: 12 September 2014 / Published: 22 September 2014
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Abstract

In this paper we investigate portfolio optimization under Value at Risk, Average Value at Risk and Limited Expected Loss constraints in a continuous time framework, where stocks follow a geometric Brownian motion. Analytic expressions for Value at Risk, Average Value at Risk and Limited Expected Loss are derived. We solve the problem of minimizing risk measures applied to portfolios. Moreover, the portfolio’s expected return is maximized subject to the aforementioned risk measures. We illustrate the effect of these risk measures on portfolio optimization by using numerical experiments. View Full-Text
Keywords: risk management; value-at-risk; average value-at-risk; limited expected loss; geometric Brownian motion; optimal portfolio strategy risk management; value-at-risk; average value-at-risk; limited expected loss; geometric Brownian motion; optimal portfolio strategy
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MDPI and ACS Style

Gambrah, P.S.N.; Pirvu, T.A. Risk Measures and Portfolio Optimization. J. Risk Financial Manag. 2014, 7, 113-129.

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