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Topics in life and disability insurance
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
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.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , 21 p.
Series
TRITA-MAT-A, 2015:09
National Category
Probability Theory and Statistics
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-175334ISBN: 978-91-7595-701-2 (print)OAI: oai:DiVA.org:kth-175334DiVA: diva2:860294
Public defence
2015-11-06, F3, Lindstedtsvägen 26, Kungliga Tekniska högskolan, Stockholm, 13:15 (English)
Opponent
Supervisors
Note

QC 20151012

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-13Bibliographically 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. A hidden Markov approach to disability insurance
Open this publication in new window or tab >>A hidden Markov approach to disability insurance
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Point and interval estimation of future disability inception and recovery rates are predominantly carried out by combining generalized linear models (GLM) 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. 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. We illustrate the modelling procedure by fitting the model to Swedish disability claims data.

National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-175337 (URN)
Note

QS 2015

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-12Bibliographically approved
3. 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
4. Aggregation of one-year risks in life and disability insurance
Open this publication in new window or tab >>Aggregation of one-year risks in life and disability insurance
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-175339 (URN)
Note

QS 2015

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-12Bibliographically approved
5. Nonlinear reserving in life insurance: aggregation and mean-field approximation
Open this publication in new window or tab >>Nonlinear reserving in life insurance: aggregation and mean-field approximation
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-175340 (URN)
Note

QS 2015

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-12Bibliographically approved

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