Portfolio optimization problem with default risk

In this paper, we consider a stochastic portfolio optimization problem with default risk on an infinite time horizon. An investor dynamically chooses a consumption rate and allocates the wealth into the securities: a perpetual defaultable bond, a money market account with the constant return and a default-free risky asset. The goal is to choose the optimal investment to maximize the infinite horizon expected discounted power utility of the consumption policies (controls). The default risk premium and the default intensity are assumed to rely on a stochastic factor formulated by a diffusion process. We study the optimal allocation and consumption policies to maximize the infinite horizon expected discounted non-log HARA utility of the consumption, and we use the dynamic programming principle to derive the Hamilton–Jacobi–Bellman (HJB) equation. Then we explore the HJB equation by employing a so-called sub–super solution approach. The optimal allocation and consumption policies are obtained in terms of the classical solution to a PDE. Finally, we get an explicit formula for the optimal control strategy. In this article The soloutions are then used in portfolio management subject to default risk and derive the optimal investment and consumption policies.

Portfolio optimization problem with default risk Keywords:

Portfolio optimization , Default risk , HJB equation , consumption policies