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Stochastic modelling in disability insurance
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two papers related to the stochastic modellingof disability insurance. In the first paper, we propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into consideration. We fit various versions of the models into Swedish disability claims data.

In the second paper, we consider a large, homogeneous portfolio oflife or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic environment. Using a conditional law of large numbers, we establish the connection between risk aggregation and claims reserving for large portfolios. Further, we derive a partial differential equation for moments of present values. Moreover, we show how statistical multi-factor intensity models can be approximated by one-factor models, which allows for solving the PDEs very efficiently. Finally, we givea numerical example where moments of present values of disabilityannuities are computed using finite difference methods.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , 9 p.
Series
Trita-MAT, ISSN 1401-2286 ; 2013:02
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-134233ISBN: 978-91-7501-964-2 (print)OAI: oai:DiVA.org:kth-134233DiVA: diva2:667607
Presentation
2013-12-19, rum 3721, Institutionen för Matematik, Lindstedtsvägen 25, KTH, Stockholm, 15:15 (English)
Opponent
Supervisors
Note

QC 20131204

Available from: 2013-12-04 Created: 2013-11-20 Last updated: 2013-12-04Bibliographically approved
List of papers
1. Stochastic modelling of disability insurance in a multi-period framework
Open this publication in new window or tab >>Stochastic modelling of disability insurance in a multi-period framework
2015 (English)In: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, no 1, 88-106 p.Article in journal (Refereed) Published
Abstract [en]

We propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into consideration. We fit various versions of the models into Swedish disability claims data.

Keyword
disability insurance, stochastic modelling, counting processes, generalized linear models
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-136247 (URN)10.1080/03461238.2013.779594 (DOI)000345384800005 ()2-s2.0-84912524177 (Scopus ID)
Note

QC 20150113. Updated from e-pub ahead of print.

Available from: 2013-12-04 Created: 2013-12-04 Last updated: 2017-12-06Bibliographically approved
2. Risk aggregation and stochastic claims reserving in disability insurance
Open this publication in new window or tab >>Risk aggregation and stochastic claims reserving in disability insurance
2014 (English)In: Insurance, Mathematics & Economics, ISSN 0167-6687, E-ISSN 1873-5959, Vol. 59, 100-108 p.Article in journal (Refereed) Published
Abstract [en]

We consider a large, homogeneous portfolio of life or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic-demographic environment. Using a conditional law of large numbers, we establish the connection between claims reserving and risk aggregation for large portfolios. Further, we derive a partial differential equation for moments of present values. Moreover, we show how statistical multi-factor intensity models can be approximated by one-factor models, which allows for solving the PDEs very efficiently. Finally, we give a numerical example where moments of present values of disability annuities are computed using finite-difference methods and Monte Carlo simulations.

Keyword
Disability insurance, stochastic intensities, condition al independence, risk aggregation, stochastic claims reserving
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-136257 (URN)10.1016/j.insmatheco.2014.09.001 (DOI)000347501100010 ()2-s2.0-84907835403 (Scopus ID)
Note

QC 20150209. Updated from manuscript to article in journal.

Available from: 2013-12-04 Created: 2013-12-04 Last updated: 2017-12-06Bibliographically approved

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