Dr. Alex Asimit

Department of Statistics

University of Toronto

Title: "Dependence and the Asymptotic Behaviour of Large Claims Reinsurance "

Insurance companies often use reinsurance as a mechanism for sharing risk, particularly
when there is the possibility of catastrophic losses. Such reinsurance comes in many
forms. Excess of loss and stop loss coverages are common, and the risks associated with
these coverages have been thoroughly studied in the literature. Two lesser-known reinsurances
are ECOMOR (excedent du cout moyen relatif) and LCR (largest claims reinsurance). This may
be due to their mathematical complexity. Under ECOMOR, the reinsurer pays the sum of the
exceedances of the l largest claims over the l+1st largest claim. Under LCR, the reinsurer
pays the sum of the l largest claims.

Asymptotic tail probabilities of the ECOMOR and LCR reinsurance amounts are obtained under
certain assumptions about the dependence structure for two classical actuarial problems. For
the first case, an extension of the classical compound Poisson risk model is considered, where
the waiting time between two consecutive claims and the forthcoming claim are no longer independent.
For the second case, a dependent portfolio of insurance contracts is analyzed.