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Coupling and Explicit Rate of Convergence in Cramer-Lundberg Approximation for Reinsurance Risk Processes
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2011 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 19-20, 3524-3539 p.Article in journal (Refereed) Published
Abstract [en]

A classical result in risk theory is the Cramer-Lundberg approximation which says that under some general conditions the exponentially normalized ruin probability converges. In this article, we state an explicit rate of convergence for the Cramer-Lundberg approximation for ruin probabilities in the case where claims are bounded, which is realistic for, e. g., reinsurance models. The method, used to get the corresponding results, is based on renewal and coupling arguments.

Place, publisher, year, edition, pages
2011. Vol. 40, no 19-20, 3524-3539 p.
Keyword [en]
Coupling method, Cramer-Lundberg approximation, Rate of convergence, Reinsurance risk process, Reinsurance ruin probability
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-66850DOI: 10.1080/03610926.2011.581176ISI: 000294892100011OAI: oai:DiVA.org:su-66850DiVA: diva2:469761
Note
authorCount :2Available from: 2011-12-27 Created: 2011-12-21 Last updated: 2017-12-08Bibliographically 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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