Dynamic Portfolio Optimization with Looping Contagion Risk

TL;DR

This paper addresses a utility maximization problem in a setting with defaultable stocks and looping contagion risk, analyzing how interconnected defaults influence optimal investment strategies and wealth distribution.

Contribution

It introduces a model where default intensities depend on stock prices, and proves the value function is the unique viscosity solution of the HJB equation.

Findings

Default intensities depend on stock prices of multiple companies.

Numerical analysis compares strategies with full and proxy intensity information.

Terminal wealth distributions vary based on utility and information used.

Abstract

In this paper we consider a utility maximization problem with defaultable stocks and looping contagion risk. We assume that the default intensity of one company depends on the stock prices of itself and other companies, and the default of the company induces immediate drops in the stock prices of the surviving companies. We prove that the value function is the unique viscosity solution of the HJB equation. We also perform some numerical tests to compare and analyse the statistical distributions of the terminal wealth of log utility and power utility based on two strategies, one using the full information of intensity process and the other a proxy constant intensity process.