Bounding basis risk using s-convex orders on Beta-unimodal distributions

Claude Lefèvre (1) , Stéphane Loisel (2) , Pierre Montesinos (2)

1 ULB - Département de Mathématique [Bruxelles]
2 SAF - Laboratoire de Sciences Actuarielle et Financière

This paper is concerned with properties of Beta-unimodal distributions and their use to assess the basis risk inherent to index-based insurance or reinsurance contracts. To this extent, we first characterize s-convex stochastic orders for Beta-unimodal distributions in terms of the Weyl fractional integral. We then determine s-convex extrema for such distributions , focusing in particular on the cases s = 2, 3, 4. Next, we define an Enterprise Risk Management framework that relies on Beta-unimodality to assess these hedge imperfections , introducing several penalty functions and worst case scenarios. Some of the results obtained are illustrated numerically via a representative catastrophe model.

Mots clés: Risk management; Parametric index; Basis risk; Beta-unimodality; s-convex stochas- tic orders; s-convex extrema

Domaines: Mathématiques [math]; Probabilités [math.PR]; Gestion et management

Claude Lefèvre, Stéphane Loisel, Pierre Montesinos. Bounding basis risk using s-convex orders on Beta-unimodal distributions. 2020. ⟨hal-02611208⟩