Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes

Romain Biard (1) , Stéphane Loisel (1) , Claudio Macci (2) , Noel Veraverbeke (3)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 DIPMAT - Dipartimento di Matematica [Roma II]
3 Center for Statistics

In the renewal risk model, we study the asymptotic behavior of the expected time-integrated negative part of the process. This risk measure has been introduced by Loisel (2005). Both heavy-tailed and light-tailed claim amount distributions are investigated. The time horizon may be finite or infinite. We apply the results to an optimal allocation problem with two lines of business of an insurance company. The asymptotic behavior of the two optimal initial reserves are computed.

Mots clés: Ruin theory; heavy-tailed and light-tailed claim size distribution; risk measure; optimal reserve allocation

Domaines: Economies et finances; Probabilités [math.PR]

Romain Biard, Stéphane Loisel, Claudio Macci, Noel Veraverbeke. Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes. 2009. ⟨hal-00372525v1⟩