A Social Insurance Network

Specialeforsvar: Sara Fuglsang Kristensen

Titel: A Social Insurance Network

Resume: This thesis considers a social insurance network. It is a new type of
insurance developed from the original purpose of insurance. In outline the
thesis explores how a social insurance network can be modelled. A possible
model for a social insurance network within a mathematical framework is
constructed, and the premium and the reinsurance premium are determined. We
apply the theory of large deviations to derive an asymptotic result for the
reinsurance premium. The established result is an asymptotic expression of the
reinsurance premium as an integral of the tail of the claim size distribution
multiplied by the expected number of claims in the network. The result is shown
for regularly varying claim size distributions, and when the claim sizes follow
a subexponential distribution. The derived asymptotic expression for the
reinsurance premium is applied in a study of a simplified social insurance
network which insures cars. This study shows that the asymptotic result holds
for a certain number of members in the network depending on the safety loading.
This suggests that the theory of large deviations contributes towards a
possible realistic social insurance network

Vejledere: Thomas Valentin Mikosch, Anders Hedegaard Jessen og Pernille Rytgaard 
Censor: Søren Asmussen