Dependence and Risk Management
Analyzing model uncertainty via a distortion of the stochastic root
In risk management it is common to model a random vector of subsequent log returns in order to analyze the distribution of their sum, e.g. for the purpose of risk measurement. Thanks to the so-called Markov regression representation any such model for a random vector can be decomposed into a sequence of independent and identically distributed random variables on the one hand, and a deterministic function f on the other hand, the latter having encoded the economic reasoning behind the model. In other words, one may distill from the model a pure random number generator. Regulatory rules demand to add a charge for the risk of potential model misspecification. To account for this, existing approaches manipulate the function f. In contrast, we propose an approach which defines model uncertainty as robustness of the function f with respect to distortions of the random number generator. This is accomplished by means of a so-called Dirichlet process and has the advantage that it is implementable in a simple and universal way, i.e. for any model.