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Nonlinear reserving in life insurance: Aggregation and mean-field approximation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0002-6608-0715
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2016 (English)In: Insurance, Mathematics & Economics, ISSN 0167-6687, E-ISSN 1873-5959, Vol. 69, 1-13 p.Article in journal (Refereed) PublishedText
Abstract [en]

We suggest a unified approach to 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
Elsevier, 2016. Vol. 69, 1-13 p.
Keyword [en]
Backward stochastic differential equation, Life insurance, Markov process, Mean-field, Multistate models, Surrender value, Thiele's equation
National Category
Mathematics Economics and Business
URN: urn:nbn:se:kth:diva-186925DOI: 10.1016/j.insmatheco.2016.04.002ISI: 000380083300001ScopusID: 2-s2.0-84963953274OAI: diva2:929291

QC 20160518

Available from: 2016-05-18 Created: 2016-05-16 Last updated: 2016-09-06Bibliographically approved

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Djehiche, BoualemLöfdahl, Björn
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