A Goal Programming Model with Satisfaction Function for Risk Management and Optimal Portfolio Diversification

TL;DR

This paper introduces a goal programming model with a satisfaction function for risk management and portfolio diversification, extending classical models to set-valued risk measures and demonstrating practical applications.

Contribution

It develops a novel goal programming approach for set-valued risk measures, enabling better risk management and portfolio diversification strategies.

Findings

Effective in practical risk management scenarios

Provides a flexible framework for set-valued risk measures

Demonstrates improved portfolio diversification

Abstract

We extend the classical risk minimization model with scalar risk measures to the general case of set-valued risk measures. The problem we obtain is a set-valued optimization model and we propose a goal programming-based approach with satisfaction function to obtain a solution which represents the best compromise between goals and the achievement levels. Numerical examples are provided to illustrate how the method works in practical situations.