Risk-Sensitive Asset Management and Cascading Defaults
研究了考虑级联违约可能性的最优风险敏感资产组合分配问题，通过求解非Lipschitz的HJB偏微分方程组，给出了最优反馈策略的显式刻画，数值分析表明投资者决策显著受传染效应影响且非单调依赖于总体风险水平。
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 quasilinear 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 significantly accounts for contagion effects when making investment decisions, and that his strategy depends nonmonotonically on the aggregate risk level.