Portfolio selection based on asymmetric Laplace distribution, coherent risk measure, and expectation-maximization estimation

Abstract

In this paper, portfolio selection problem is studied under Asymmetric Laplace Distribution(ALD) framework. Asymmetric Laplace distribution is able to capture tail-heaviness, skewness, andleptokurtosis observed in empirical financial data that cannot be explained by traditional Gaussiandistribution. Under Asymmetric Laplace distribution framework, portfolio selection methods basedon di erent risk measures are discussed. Moreover, we derived the Expectation-Maximization (EM)procedure for parameter estimation of Asymmetric Laplace distribution. Performance of the proposedmethod is illustrated via extensive simulation studies. Two real data examples are complemented toconfirm that the Asymmetric Laplace distribution based portfolio selection models are effcient.

Keywords

• portfolio selection| Asymmetric Laplace distributions| EM procedure| tail-heaviness| Skewness