Basis risk management and randomly scaled uncertainty

Abstract

This paper proposes a method for quantifying the basis risk present in index-based insurance. It applies when the inherent uncertainty is represented by a randomly scaled variable. This turns out to be a reasonable assumption in a number of practical situations. Several properties of such a variable are first briefly studied. Their order in the s-convex sense is discussed and the associated extreme distributions are obtained to generate the worst situations. In each scenario, the basis risk consequences are then assessed using a penalty function that takes into account the risk tolerances of the protection buyer. Basis risk limits for a fixed budget can also be set. The proposed approach is illustrated by a few simple examples.