Speaker(s): Ralf Korn (Technische Universität Kaiserslautern)
In classical continuous- or discrete-time portfolio optimization the market model underlying the optimization problem is completely specified. In contrast to that, stress scenarios are an essential tool to judge the solvability of an insurance company and also its ability to give insurance even in the face of extremely unpleasant or unexpected events. We will show how the use of stress scenarios can be introduced into continuous-time portfolio optimization. Their use will be linked to the worst-case portfolio optimization approach as introduced in Korn and Wilmott (2002) and further developed in Korn (2005), Korn and Menkens (2005), Korn and Steffensen (2007) , Desmettre et al. (2015) or Seifried (2010).
The occurrence of a stress scenario will not be assigned a probability. It will be treated as an event that has Knightian uncertainty. As a consequence, the solution of the problem under a possible stress scenario leads to a combination of an unconstrained portfolio optimization problem and the problem of finding so-called indifference strategies. These strategies make the investor indifferent between the occurrence of the stress scenario and its non-occurrence. These strategies can be obtained by solving a series of (typically) ordinary differential equations. The form of the resulting worst-case optimal strategies often resemble traditional life-styling in pension strategies. They thus underpin a practically applied method with a scientific argument