Risk Sensitive Asset Management and Cascading Defaults

Abstract

We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility of cascading defaults. Default events have an impact on the distress state of the surviving stocks in the portfolio. We study the recursive system of non-Lipschitz quasi-linear parabolic HJB-PDEs associated with the value function of the control problem in the different default states of the economy. We show the existence of a classical solution to this system via super-sub solution techniques and give an explicit characterization of the optimal feedback strategy in terms of the value function. We prove a verification theorem establishing the uniqueness of the solution. A numerical analysis indicates that the investor accounts for contagion effects when making investment decisions, reduces his risk exposure as he becomes more sensitive to risk, and that his strategy depends non-monotonically on the aggregate risk level.

Keywords: risk-sensitive control, cascading defaults, contagion, asset management

JEL Classification: C32, C52, D81, D83, D84