The sparse method of simulated quantiles: An application to portfolio optimization

Abstract

The sparse multivariate method of simulated quantiles (S-MMSQ) is applied to solve a portfolio optimization problem under value-at-risk constraints where the joint returns follow a multivariate skew-elliptical stable distribution. The S-MMSQ is a simulation-based method that is particularly useful for making parametric inference in some pathological situations where the maximum likelihood estimator is difficult to compute. The method estimates parameters by minimizing the distance between quantile-based statistics evaluated on true and synthetic data, simulated from the postulated model, penalized by adding the smoothly clipped absolute deviation 1 -penalty in order to achieve sparsity. The S-MMSQ aims to efficiently handle the problem of estimating large-dimensional distributions with intractable likelihood, such as the stable distributions that have been widely applied in finance to model financial returns. KEYWORDSportfolio optimization, SCAD, skew-elliptical stable distribution, sparse method of simulated quantiles, sparse regularization

Forecasting VaR and ES using a joint quantile regression and implications in portfolio allocation

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Quantile Mixed Hidden Markov Models for Multivariate Longitudinal Data: An Application to Children's Strengths and Difficulties Questionnaire Scores

“…When multivariate response variables are concerned, however, the univariate quantile regression method does not straightforwardly extend to higher dimensions since there is no ‘natural’ ordering in a p ‐dimensional space, for p > 1. As a consequence, the search for a satisfactory notion of multivariate quantile has led to a flourishing literature on this topic despite its definition is still a debatable issue (see Alfò et al, 2021; Chakraborty, 2003; Charlier et al, 2020; Chavas, 2018; Hallin et al, 2010; Koenker et al, 2017; Kong & Mizera, 2012; Merlo et al, 2021; Stolfi et al, 2018 and the references therein for relevant studies). Recently, Petrella and Raponi (2019) generalized the AL distribution inferential approach of the univariate quantile regression to a multivariate framework by using the multivariate asymmetric Laplace (MAL) distribution defined in Kotz et al (2012).…”