Portfolio Choice with Market-Credit Risk Dependencies

TL;DR

This paper develops a model for optimal investment and consumption considering dependencies between market and credit risks, providing explicit strategies and analyzing their sensitivity to various risk factors.

Contribution

It introduces a novel approach to handle market-credit risk dependencies using semi-linear PDEs and derives explicit optimal strategies with numerical sensitivity analysis.

Findings

Explicit optimal strategies derived from semi-linear PDEs

Strategies are sensitive to risk aversion, default risk, and volatility

Existence and uniqueness of solutions established for the PDE system

Abstract

We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale approach and analyze the recursive system of nonlinear Hamilton-Jacobi-Bellman equations associated with the dual problem. We transform such a system into an equivalent system of semi-linear PDEs, for which we establish existence and uniqueness of a bounded global classical solution. We obtain explicit representations for the optimal strategy, consumption path and wealth process, in terms of the solution to the recursive system of semi-linear PDEs. We numerically analyze the sensitivity of the optimal investment strategies to risk aversion, default risk and volatility.