Erland Ekheden: Catastrophe, Ruin and Death

This thesis gives some perspectives on insurance mathematics related to life insurance and / or reinsurance. Catastrophes and large accidents resulting in many lost lives are unfortunately known to happen over and over again. A new model for the occurrence of catastrophes is presented; it models the number of catastrophes, how many lives that are lost, how many lost lives that are insured by a specific insurer, the cost of the resulting claims and it makes it possible to calculate the price of reinsurance contracts linked to catastrophic events.

Ruin is the result if claims exceed initial capital and the premiums collected by an insurance company. We analyze the Cramér-Lundberg approximation for the ruin probability and give an explicit rate of convergence in the case were claims are bounded by some upper limit. Death is known to be the only thing that is certain in life. Individual life spans are however random, models for and statistics of mortality are important for, amongst others, life insurance companies whose payments ultimately depend on people being alive or dead. We analyse the stochasticity of mortality and perform a variance decomposition were the variation in mortality data is either explained by the covariates age and time, unexplained systematic variation or random noise due to a finite population. We suggest a mixed regression model for mortality and fit it to data from the US and Sweden, including prediction intervals of future mortalities.