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Multivariate Time Series Modeling, Estimation and Prediction of Mortalities
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.ORCID-id: 0000-0001-9746-0756
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
(Engelska)Artikel i tidskrift (Refereegranskat) Submitted
Abstract [en]

We introduce a mixed regression model for morality data whichcan be decomposed into a deterministic trend component explainedby the covariates age and calendar year, a multivariate Gaussian timeseries part not explained by the covariates, and binomial risk. Datacan be analyzed by means of a simple logistic regression model whenthe multivariate Gaussian time series component is absent and there isno overdispersion, as in Ekheden and Hössjer (2014). In this paper werather allow for overdispersion and the mixed regression model is ttedto mortality data from the United States and Sweden, with the aim toprovide prediction and condence intervals for future mortality, as wellas smoothing historical data, using the best linear unbiased predictor.We nd that the form of the Gaussian time series has a large impact onthe width of the prediction intervals, and it poses some new questionson proper model selection.

Nyckelord [en]
Best linear unbiased predictor, generalized least squares, longevity, mortality prediction, multivariate time series, overdispersion
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematisk statistik
Identifikatorer
URN: urn:nbn:se:su:diva-103163OAI: oai:DiVA.org:su-103163DiVA, id: diva2:715998
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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