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Risk Measures and Portfolio Optimization

Author

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  • Priscilla Serwaa Nkyira Gambrah

    (Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4L8, Canada)

  • Traian Adrian Pirvu

    (Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4L8, Canada)

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.

Suggested Citation

  • Priscilla Serwaa Nkyira Gambrah & Traian Adrian Pirvu, 2014. "Risk Measures and Portfolio Optimization," JRFM, MDPI, vol. 7(3), pages 1-17, September.
    • Handle: RePEc:gam:jjrfmx:v:7:y:2014:i:3:p:113-129:d:40516
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    References listed on IDEAS

    as
    1. Traian A. Pirvu, 2007. "Portfolio optimization under the Value-at-Risk constraint," Quantitative Finance, Taylor & Francis Journals, vol. 7(2), pages 125-136.
    2. Gordana Dmitrašinović-Vidović & Antony Ware, 2006. "Asymptotic behaviour of mean-quantile efficient portfolios," Finance and Stochastics, Springer, vol. 10(4), pages 529-551, December.
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    4. Xie, Shuxiang & Li, Zhongfei & Wang, Shouyang, 2008. "Continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 943-953, June.
    5. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
    6. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    7. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    8. Markowitz, Harry M, 1991. "Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-477, June.
    9. Susanne Emmer & Claudia Klüppelberg & Ralf Korn, 2001. "Optimal Portfolios with Bounded Capital at Risk," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 365-384, October.
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    Citations

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    Cited by:

    1. Naomi Pandiangan & Sukono Sukono & Endang Soeryana Hasbullah, 2021. "Quadratic Investment Portfolio Based on Value-at-risk with Risk-Free Assets: For Stocks of the Mining and Energy Sector," International Journal of Energy Economics and Policy, Econjournals, vol. 11(4), pages 175-184.
    2. Farzad Pourbabaee & Minsuk Kwak & Traian A. Pirvu, 2014. "Risk minimization and portfolio diversification," Papers 1411.6657, arXiv.org, revised Dec 2014.
    3. S. Geissel & H. Graf & J. Herbinger & F. T. Seifried, 2022. "Portfolio optimization with optimal expected utility risk measures," Annals of Operations Research, Springer, vol. 309(1), pages 59-77, February.
    4. Feghhi Kashani , Mohammad & Mohebimajd , Ahmadreza, 2021. "Outperformance Testing of a Dynamic Assets Portfolio Selection Supplemented with a Continuous Paths Levy Process," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 16(2), pages 253-282, June.
    5. Farzad Pourbabaee & Minsuk Kwak & Traian A. Pirvu, 2016. "Risk minimization and portfolio diversification," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1325-1332, September.
    6. Chunwei Wang & Naidan Deng & Silian Shen, 2022. "Numerical Method for a Perturbed Risk Model with Proportional Investment," Mathematics, MDPI, vol. 11(1), pages 1-27, December.
    7. Gabrielli, Paolo & Aboutalebi, Reyhaneh & Sansavini, Giovanni, 2022. "Mitigating financial risk of corporate power purchase agreements via portfolio optimization," Energy Economics, Elsevier, vol. 109(C).
    8. Theofanis Petropoulos & Konstantinos Liapis & Eleftherios Thalassinos, 2023. "Optimal Structure of Real Estate Portfolio Using EVA: A Stochastic Markowitz Model Using Data from Greek Real Estate Market," Risks, MDPI, vol. 11(2), pages 1-19, February.
    9. H. Fink & S. Geissel & J. Herbinger & F. T. Seifried, 2019. "Portfolio Optimization with Optimal Expected Utility Risk Measures," Working Paper Series 2019-07, University of Trier, Research Group Quantitative Finance and Risk Analysis.

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