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Stochastic modelling of disability insurance in a multi-period framework
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.ORCID-id: 0000-0002-6608-0715
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
2015 (Engelska)Ingår i: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, nr 1, s. 88-106Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
2015. nr 1, s. 88-106
Nyckelord [en]
disability insurance, stochastic modelling, counting processes, generalized linear models
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
URN: urn:nbn:se:kth:diva-136247DOI: 10.1080/03461238.2013.779594ISI: 000345384800005Scopus ID: 2-s2.0-84912524177OAI: oai:DiVA.org:kth-136247DiVA, id: diva2:675636
Anmärkning

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

Tillgänglig från: 2013-12-04 Skapad: 2013-12-04 Senast uppdaterad: 2017-12-06Bibliografiskt granskad
Ingår i avhandling
1. Stochastic modelling in disability insurance
Öppna denna publikation i ny flik eller fönster >>Stochastic modelling in disability insurance
2013 (Engelska)Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Stockholm: KTH Royal Institute of Technology, 2013. s. 9
Serie
Trita-MAT, ISSN 1401-2286 ; 2013:02
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
urn:nbn:se:kth:diva-134233 (URN)978-91-7501-964-2 (ISBN)
Presentation
2013-12-19, rum 3721, Institutionen för Matematik, Lindstedtsvägen 25, KTH, Stockholm, 15:15 (Engelska)
Opponent
Handledare
Anmärkning

QC 20131204

Tillgänglig från: 2013-12-04 Skapad: 2013-11-20 Senast uppdaterad: 2013-12-04Bibliografiskt granskad
2. Topics in life and disability insurance
Öppna denna publikation i ny flik eller fönster >>Topics in life and disability insurance
2015 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

This thesis consists of five papers, presented in Chapters A-E, on topics in life and disability insurance. It is naturally divided into two parts, where papers A and B discuss disability rates estimation based on historical claims data, and papers C-E discuss claims reserving, risk management and insurer solvency.In Paper A, disability inception and recovery probabilities are modelled in a generalized linear models (GLM) framework. For prediction of future disability rates, it is customary to combine GLMs with time series forecasting techniques into a two-step method involving parameter estimation from historical data and subsequent calibration of a time series model. This approach may in fact lead to both conceptual and numerical problems since any time trend components of the model are incoherently treated as both model parameters and realizations of a stochastic process. In Paper B, we suggest that this general two-step approach can be improved in the following way: First, we assume a stochastic process form for the time trend component. The corresponding transition densities are then incorporated into the likelihood, and the model parameters are estimated using the Expectation-Maximization algorithm.In Papers C and D, we consider a large 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 the Conditional Law of Large Numbers (CLLN), we establish the connection between claims reserving and risk aggregation for large portfolios. Moreover, we show how statistical multi-factor intensity models can be approximated by one-factor models, which allows for computing reserves and capital requirements efficiently. Paper C focuses on claims reserving and ultimate risk, whereas the focus of Paper D is on the one-year risks associated with the Solvency II directive.In Paper E, we consider claims reserving for life insurance policies with reserve-dependent payments driven by multi-state Markov chains. The associated prospective reserve is formulated as a recursive utility function using the framework of backward stochastic differential equations (BSDE). We show that the prospective reserve satisfies a nonlinear Thiele equation for Markovian BSDEs when the driver is a deterministic function of the reserve and the underlying Markov chain. Aggregation of prospective reserves for large and homogeneous insurance portfolios is considered through mean-field approximations. We show that the corresponding prospective reserve satisfies a BSDE of mean-field type and derive the associated nonlinear Thiele equation.

Ort, förlag, år, upplaga, sidor
Stockholm: KTH Royal Institute of Technology, 2015. s. 21
Serie
TRITA-MAT-A ; 2015:09
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
Tillämpad matematik och beräkningsmatematik
Identifikatorer
urn:nbn:se:kth:diva-175334 (URN)978-91-7595-701-2 (ISBN)
Disputation
2015-11-06, F3, Lindstedtsvägen 26, Kungliga Tekniska högskolan, Stockholm, 13:15 (Engelska)
Opponent
Handledare
Anmärkning

QC 20151012

Tillgänglig från: 2015-10-12 Skapad: 2015-10-12 Senast uppdaterad: 2015-10-13Bibliografiskt granskad

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Djehiche, Boualem

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