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Pricing catastrophe risk in life (re)insurance
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0001-9746-0756
Stockholm University, Faculty of Science, Department of Mathematics.
2014 (English)In: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, Vol. 2014, no 4, 352-367 p.Article in journal (Refereed) Published
Abstract [en]

What is the catastrophe risk a life insurance company faces? What is the correct price of a catastrophe cover? During a review of the current standard model, due to Strickler, we found that this model has some serious shortcomings. We therefore present a new model for the pricing of catastrophe excess of loss cover (Cat XL). The new model for annual claim cost C is based on a compound Poisson processof catastrophe costs. To evaluate the distribution of the cost of each catastrophe, we use the Peaks Over Threshold model for the total number of lost lives in each catastrophe and the beta binomial model for the proportion of these corresponding to customers of the insurance company. To be able to estimate the parameters of the model, international and Swedish data were collected and compiled,listing accidents claiming at least twenty and four lives, respectively. Fitting the new model to data, we find the fit to be good. Finally we give the price of a Cat XL contract and perform a sensitivity analysis of how some of the parameters affect the expected value and standard deviation of the cost and thus the price.

Place, publisher, year, edition, pages
London: Taylor & Francis, 2014. Vol. 2014, no 4, 352-367 p.
Keyword [en]
catastrophe excess of loss; life reinsurance; catastrophe model; catastrophe data; Cat XL; POT-model; Solvency II; internal models
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-103151DOI: 10.1080/03461238.2012.695747ISI: 000333884000004OAI: oai:DiVA.org:su-103151DiVA: diva2:715958
Available from: 2014-05-07 Created: 2014-05-07 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Catastrophe, Ruin and Death - Some Perspectives on Insurance Mathematics
Open this publication in new window or tab >>Catastrophe, Ruin and Death - Some Perspectives on Insurance Mathematics
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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 unfortunatley known to happen over and over again. A new model for the occurence 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 and the cost of the resulting claims, this  makes it possible to calculate the price of reinsurance contracts linked to catastrophic events. 

Ruin is the result if claims exceed inital 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 imortant for, amongst others, life insurance companies whose payments ultimatley 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.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2014. 36 p.
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-103165 (URN)978-91-7447-935-5 (ISBN)
Public defence
2014-06-05, room 14, house 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: In press. Paper 4: Submitted.

Available from: 2014-05-14 Created: 2014-05-07 Last updated: 2014-05-09Bibliographically approved

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