OPTIMAL PORTFOLIO CHOICE WITH CRASH AND DEFAULT RISK

We consider the worst-case scenario portfolio approach, introduced by by Korn & Wilmott (2002), in a multi-asset setting, where asset defaults can occur in addition to asset crashes. In our model, the strictly risk-averse investor does not know which asset is affected by the worst-case scenario. Based on a reformulation of the value function we define the set of minimum constant portfolio processes. We prove the existence of such a process that solves the worst-case crash/default portfolio problem. In particular, we prove the existence of a portfolio process that is optimal for the investor and at the same time makes him/her indifferent to the time of occurrence of the worst possible crash or default scenario. The optimal portfolios are derived from solutions of non-linear differential equations. Therefore, we construct an algorithmic framework to analyze selected examples. These examples show the importance of adapting the portfolio process when considering such worst-case scenarios in the investment problem.