Robust Optimal Portfolio in a Mixture Setting with Partial Ambiguity

TL;DR

This paper develops a robust portfolio optimization method under partial ambiguity in mixture risk models, using a convex-nonconcave minimax approach with convergence guarantees and numerical validation.

Contribution

It introduces a novel robust optimization framework for mixture risk models with partial ambiguity, employing a projected subgradient descent algorithm and analyzing convergence rates.

Findings

The proposed method effectively handles partial ambiguity in risk models.

Convergence rate is $O(1/ oot{k})$, with potential for exponential convergence.

Numerical examples demonstrate the approach's efficiency and geometric convergence.

Abstract

Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or known, and others, along with their weights, are not. Our paper addresses two robust portfolio optimization problems with partial ambiguity, where the loss function involves either variance or conditional value-at-risk (CVaR). We use a projected subgradient descent algorithm to solve the optimization problems. The problem reduces to a convex-nonconcave minimax problem. We show that, while the general problem converges at an $O(1/\sqrt{k})$ rate, where $k$ denotes the number of iterations, exponential convergence is possible in some cases. Lastly, we provide numerical examples to show the effectiveness of our approach and the attainment of a geometric convergence rate. This work aims to provide more effective solutions for actuarial decision-making under model uncertainty.