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Analysis of the Stochasticity of Mortality Using Variance Decomposition
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: Modern Problems in Insurance Mathematics / [ed] Dmitri Silvestrov and Anders Martin-Löf, Springer Publishing Company, 2014, 199-222 p.Chapter in book (Refereed)
Abstract [en]

We analyse the stochasticity in mortality data from the USA, the UK and Sweden, and in particular to which extent mortality rates are explained by systematic variation, due to various risk factors, and random noise. We formalise this in terms of a mixed regression model with a logistic link function, and decomposethe variance of the observations into three parts: binomial risk, the variance due to random mortality variation in a finite population, systematic risk explained by the covariates and unexplained systematic risk, variance that comes from real changes in mortality rates, not captured by the covariates. The fraction of unexplained variance caused by binomial risk provides a limit in terms of the resolution that can be achieved by a model. This can be used as a model selection tool for selecting the number of covariates and regression parameters of the deterministic part of the regression function, and for testing whether unexplained systematic variation should be explicitly modelled or not. We use a two-factor model with ageand calendar year as covariates, and perform the variance decomposition for a simple model with a linear time trend on the logit scale. The population size turns out to be crucial, and for Swedish data, the simple model works surprisingly well, leaving only a small fraction of unexplained systematic risk, whereas for the UK and the USA, the amount of unexplained systematic risk is larger, so that more elaborate models might work better.

Place, publisher, year, edition, pages
Springer Publishing Company, 2014. 199-222 p.
Series
EAA, 7879
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-103153DOI: 10.1007/978-3-319-06653-0_13ISBN: 9783319066523 (print)OAI: oai:DiVA.org:su-103153DiVA: diva2:715999
Available from: 2014-05-07 Created: 2014-05-07 Last updated: 2014-07-03Bibliographically 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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Publisher's full texthttp://www.springer.com/new+%26+forthcoming+titles+(default)/book/978-3-319-06652-3

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