Portfolio Selection Problem with a Non-Zero Recovery Bond

Abstract

In an earlier paper Liang [1], the author applies the framework of Merton [2] to a market model that consists of a no-recovery defaultable bond as well as a riskless asset. In this paper, we extend the result of Liang [1] for a non-zero recovery bond.

We study an optimization problem of consumption and investment strategy for an investor who can invest in a riskless asset and a defaultable asset with a positive recovery. Merton [2] is the first to formulate and solve such an optimization problem, and many researchers have extended and generalized the model of consumption and investment. However, optimization problems with defaultable assets have been rarely studied, though it is so important in today's financial market. This paper applies the framework of original Merton's model to a new market model that consists of a recovery bond as well as a riskless asset. Under the assumption that the defaultable asset's price is modeled as a geometric Brownian motion with an unpredictable jump to a positive value, the optimal problem is reformulated and analytically solved.