Portfolio Selection under Multivariate Merton Model with Correlated Jump Risk

TL;DR

This paper develops a more efficient method for portfolio optimization under a multivariate Merton model with correlated jumps, using closed-form bounds for CVaR to replace computationally intensive simulations.

Contribution

It introduces a novel closed-form approach for CVaR-based portfolio optimization in models with dependent jumps, improving computational efficiency.

Findings

The proposed method reduces computation time significantly.

It provides accurate bounds for CVaR in complex jump models.

The approach is applicable to real-world portfolio management scenarios.

Abstract

Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is measured by the Condition-Value-at-Risk ($CVaR$). Solving the portfolio optimization problem by Monte Carlo simulation often requires intensive and time-consuming computation; hence a faster and more efficient portfolio optimization method based on closed-form comonotonic bounds for the risk measure $CVaR$ of the terminal wealth is proposed.