Properties of a risk measure derived from the expected area in red

Stéphane Loisel (1) , Julien Trufin (2)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 Ecole d'Actuariat

This paper studies a new risk measure derived from the expected area in red introduced in Loisel (2005). Specifically, we derive various properties of a risk measure defined as the smallest initial capital needed to ensure that the expected time-integrated negative part of the risk process on a fixed time interval [0; T] (T can be infinite) is less than a given predetermined risk limit. We also investigate the optimal risk limit allocation: given a risk limit set at company level for the sum of the expected areas in red of all lines, we determine the way(s) to allocate this risk limit to the subsequent business lines in order to minimize the overall capital needs.

Mots clés: Ruin probability; risk measure; expected area in red; stochastic ordering; risk limit

Domaines: Economies et finances; Probabilités [math.PR]; Gestion des risques [q-fin.RM]

Stéphane Loisel, Julien Trufin. Properties of a risk measure derived from the expected area in red. Insurance: Mathematics and Economics, 2014, 55, pp.191-199. ⟨hal-00870224⟩