Stochastic modelling in disability insurance
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
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.
Trita-MAT, ISSN 1401-2286 ; 2013:02
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-134233ISBN: 978-91-7501-964-2OAI: oai:DiVA.org:kth-134233DiVA: diva2:667607
2013-12-19, rum 3721, Institutionen för Matematik, Lindstedtsvägen 25, KTH, Stockholm, 15:15 (English)
Steffensen, Mogens, Professor
Djehiche, Boualem, Professor
QC 201312042013-12-042013-11-202013-12-04Bibliographically approved
List of papers