A stochastic reachability approach to portfolio construction in finance industry

TL;DR

This paper introduces a stochastic reachability method for portfolio construction that aims to maximize the probability of staying within desired value ranges, addressing limitations of traditional models like Markowitz.

Contribution

It proposes a novel stochastic reachability-based approach for portfolio optimization, improving upon classical methods by focusing on probabilistic target set adherence.

Findings

The method increases the probability of portfolio staying within target ranges.

Case study shows improved performance over traditional approaches.

Demonstrates practical benefits in US market portfolio management.

Abstract

In finance industry portfolio construction deals with how to divide the investors' wealth across an asset-classes' menu in order to maximize the investors' gain. Main approaches in use at the present are based on variations of the classical Markowitz model. However, recent evolutions of the world market showed limitations of this method and motivated many researchers and practitioners to study alternative methodologies to portfolio construction. In this paper we propose one approach to optimal portfolio construction based on recent results on stochastic reachability, which overcome some of the limits of current approaches. Given a sequence of target sets that the investors would like their portfolio to stay within, the optimal portfolio allocation is synthesized in order to maximize the joint probability for the portfolio value to fulfill the target sets requirements. A case study in the US market is given which shows benefits from the proposed methodology in portfolio construction. A comparison with traditional approaches is included.