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Mean-CVaR portfolio selection: a nonparametric estimation framework. (English) Zbl 1349.91323
Summary: In this paper, we use Conditional Value-at-Risk (CVaR) to measure risk and adopt the methodology of nonparametric estimation to explore the mean-CVaR portfolio selection problem. First, we obtain the estimated calculation formula of CVaR by using the nonparametric estimation of the density of the loss function, and formulate two nonparametric mean-CVaR portfolio selection models based on two methods of bandwidth selection. Second, in both cases when short-selling is allowed and forbidden, we prove that the two nonparametric mean-CVaR models are convex optimization problems. Third, we show that when CVaR is solved for, the corresponding VaR can also be obtained as a by-product. Finally, we present a numerical example with Monte Carlo simulations to demonstrate the usefulness and effectiveness of our results, and compare our nonparametric method with the popular linear programming method.

91G70 Statistical methods; risk measures
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G10 Portfolio theory
91B30 Risk theory, insurance (MSC2010)
91G60 Numerical methods (including Monte Carlo methods)
65C05 Monte Carlo methods
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