Risk Sensitive Asset Management and Cascading Defaults

Much of the literature on asset management considers default-free assets with continuously varying prices across time. Most assets are, however, subject to default and jumps in values that are correlated and can lead to cascades. This talk will describe a model of an optimal risk-sensitive portfolio allocation problem in this setting, which explicitly accounts for the interaction between market and credit risk. The model includes a recursive dependence between the non-Lipschitz quasi-linear parabolic HJB-PDEs associated with the default states of the portfolio. The speaker will show the existence of a classical solution to this system via super-sub solution techniques and will give an explicit characterization of the optimal feedback strategy and present a numerical analysis that indicates that the investor accounts for contagion effects when making investment decisions, reducing risk exposure and extracting utility as risk sensitivity increases, and that the strategy depends non-monotonically on the aggregate risk level.