Multivariate Portfolio Choice Via Quantiles

Abstract

We first show how the quantile approach used for univariate optimal portfolio choice can also be useful when dealing with the multivariate case. Specifically, when a related multivariate risk sharing problem (in the absence of a financial market) can be solved explicitly, then multivariate optimal portfolio choice is shown to reduce to a one-dimensional problem that can be dealt with using the quantile approach. We use this finding to develop an efficient algorithm to determine optimal portfolios. We also develop a numerical approach that makes it possible to obtain approximate solutions for general multivariate portfolio selection problems.

Keywords: decision analysis, multivariate optimal portfolio choice, quantile approach, multivariate utility, cost-efficiency.