Optimal Multivariate Financial Decision Making

Abstract

Agents who pursue optimal portfolio choice by optimizing a univariate objective (e.g., an expected utility) obtain optimal payoffs that are increasing with each other (situation of no diversification). This situation may lead to an undesirable level of systemic risk for society. A regulator may consider a global perspective and aim to enforce diversification among the various portfolios by optimizing a suitable multivariate objective. We explain that optimal solutions satisfy a notion of multivariate cost-efficiency and provide an algorithm to obtain multivariate cost-efficient payoffs.
We also assess the cost of diversification and provide the strategy that the regulator should pursue for obtaining the desired level of diversification.

Keywords: Cost-efficiency, multivariate utility, multivariate preferences, diversification, systemic risk