A discussion of stochastic dominance and mean-CVaR optimal portfolio problems based on mean-variance-mixture models
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The classical Markowitz mean-variance model uses variance as a risk measure and calculates frontier portfolios in closed form by using standard optimization techniques. For general mean-risk models such closed form optimal portfolios are difficult to obtain. In this note, we obtain closed form expressions for frontier portfolios under mean-CVaR criteria when return vectors have normal mean-variance mixture (NMVM) distributions. To achieve this goal, we first present necessary conditions for stochastic dominance within the class of one dimensional NMVM models and then we apply them to portfolio optimization problems. Our main result in this paper states that when return vectors follow NMVM distributions the associated mean- CVaR frontier portfolios can be obtained by optimizing a Markowitz mean-variance model with an appropriately adjusted return vector
Date: 2022-02, Revised 2022-08
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