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Coherent Risk Measures And Normal Mixture Distributions With Applications In Portfolio Optimization

Author

Listed:
  • XIANG SHI

    (Department of Applied Mathematics and Statistics, Stony Brook University, New York, USA)

  • YOUNG SHIN KIM

    (College of Business, Stony Brook University, New York, USA)

Abstract

This paper investigates the coherent risk measure of a class of normal mixture distributions which are widely-used in finance. The main result shows that the mean-risk portfolio optimization problem with these normal mixture distributions can be reduced to a quadratic programming problem which has closed form of solution by fixing the location parameter and skewness parameter. In addition, we show that the efficient frontier of the portfolio optimization problem can be extended to three dimensions in this case. The worst-case value-at-risk in the robust portfolio optimization can also be calculated directly. Finally, the conditional value-at-risk (CVaR) is considered as an example of coherent risk measure. We obtain the marginal contribution to risk for a portfolio based on the normal mixture model.

Suggested Citation

  • Xiang Shi & Young Shin Kim, 2021. "Coherent Risk Measures And Normal Mixture Distributions With Applications In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 1-18, June.
    • Handle: RePEc:wsi:ijtafx:v:24:y:2021:i:04:n:s0219024921500199
    DOI: 10.1142/S0219024921500199
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    Cited by:

    1. Tiantian Li & Young Shin Kim & Qi Fan & Fumin Zhu, 2021. "Aumann–Serrano index of risk in portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 197-217, October.
    2. Nuerxiati Abudurexiti & Kai He & Dongdong Hu & Svetlozar T. Rachev & Hasanjan Sayit & Ruoyu Sun, 2021. "Portfolio analysis with mean-CVaR and mean-CVaR-skewness criteria based on mean-variance mixture models," Papers 2111.04311, arXiv.org, revised Feb 2023.

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