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Pricing catastrophe risk in life (re)insurance
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.ORCID-id: 0000-0001-9746-0756
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
2014 (Engelska)Ingår i: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, Vol. 2014, nr 4, s. 352-367Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
London: Taylor & Francis, 2014. Vol. 2014, nr 4, s. 352-367
Nyckelord [en]
catastrophe excess of loss; life reinsurance; catastrophe model; catastrophe data; Cat XL; POT-model; Solvency II; internal models
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematisk statistik
Identifikatorer
URN: urn:nbn:se:su:diva-103151DOI: 10.1080/03461238.2012.695747ISI: 000333884000004OAI: oai:DiVA.org:su-103151DiVA, id: diva2:715958
Tillgänglig från: 2014-05-07 Skapad: 2014-05-07 Senast uppdaterad: 2022-02-23Bibliografiskt granskad
Ingår i avhandling
1. Catastrophe, Ruin and Death - Some Perspectives on Insurance Mathematics
Öppna denna publikation i ny flik eller fönster >>Catastrophe, Ruin and Death - Some Perspectives on Insurance Mathematics
2014 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Stockholm: Department of Mathematics, Stockholm University, 2014. s. 36
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematisk statistik
Identifikatorer
urn:nbn:se:su:diva-103165 (URN)978-91-7447-935-5 (ISBN)
Disputation
2014-06-05, room 14, house 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (Engelska)
Opponent
Handledare
Anmärkning

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.

Tillgänglig från: 2014-05-14 Skapad: 2014-05-07 Senast uppdaterad: 2022-02-23Bibliografiskt granskad

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Ekheden, ErlandHössjer, Ola

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