COHERENT RISK MEASURES AND NORMAL MIXTURE DISTRIBUTIONS WITH APPLICATIONS IN PORTFOLIO OPTIMIZATION

Xiang Shi and Young Shin Kim ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2021, vol. 24, issue 04, 1-18

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.

Keywords: Coherent risk measure; CVaR; normal mixture distribution; generalized hyperbolic distribution; portfolio optimization; worst-case risk (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024921500199

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