Basis Risk Management in an Index-Based Insurance Framework under Randomly Scaled Uncertainty.

Summary This paper is concerned with the quantification of basis risk in index-based insurance products using randomly scaled variables. To this extent, we first discuss the shape, the unimodality and the symmetry of randomly scaled variables depending on the distribution of the random scaling factor using Mellin transform. We explicitly obtain the distribution of a randomly scaled variable when the random scaling factor is either uniformly distributed or of Beta type. We then determine s-convex extremal distributions for randomly scaled variables and discuss the way of comparing it. Next, we define an Enterprise Risk Management framework that relies on randomly scaled variables to assess basis risk, introducing the class of generalized penalty functions. This ERM framework allows for setting up basis risk limits to eventually determine a Basis Risk Capital Requirement. The results are illustrated with particular cases that carefully challenge the methodology.