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Asymptotics of Ruin Probabilities for Perturbed Discrete Time Risk Processes
Stockholm University, Faculty of Science, Department of Mathematics.
2014 (English)In: Modern Problems in Insurance Mathematics / [ed] Dmitrii Silvestrov, Anders Martin-Löf, Springer, 2014, 95-112 p.Chapter in book (Refereed)
Abstract [en]

We consider the problem of approximating the infinite time horizon ruin probabilities for discrete time risk processes. The approach is based on asymptotic results for non-linearly perturbed discrete time renewal equations. Under some moment conditions on the claim distributions, the approximations take the form of exponential asymptotic expansions with respect to the perturbation parameter. We show explicitly how the coefficients of these expansions can be computed as functions of the coefficients of the expansions of local characteristics for perturbed risk processes.

Place, publisher, year, edition, pages
Springer, 2014. 95-112 p.
Series
EAA Series, ISSN 1869-6929
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-95469DOI: 10.1007/978-3-319-06653-0_7ISBN: 978-3-319-06652-3 (print)ISBN: 978-3-319-06653-0 (print)OAI: oai:DiVA.org:su-95469DiVA: diva2:660274
Available from: 2013-10-29 Created: 2013-10-29 Last updated: 2016-04-28Bibliographically approved
In thesis
1. Asymptotic Expansions for Perturbed Discrete Time Renewal Equations
Open this publication in new window or tab >>Asymptotic Expansions for Perturbed Discrete Time Renewal Equations
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we study the asymptotic behaviour of the solution of a discrete time renewal equation depending on a small perturbation parameter. In particular, we construct asymptotic expansions for the solution of the renewal equation and related quantities. The results are applied to studies of quasi-stationary phenomena for regenerative processes and asymptotics of ruin probabilities for a discrete time analogue of the Cramér-Lundberg risk model.

Place, publisher, year, edition, pages
Department of Mathematics, 2013. 19 p.
Keyword
Renewal equation, Perturbation, Asymptotic expansion, Regenerative process, Quasi-stationary distribution, Risk process, Ruin probability
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:su:diva-95490 (URN)
Presentation
2013-11-20, 306, Matematiska institutionen, Hus 6, Kräftriket, Stockholm, 15:15 (English)
Opponent
Supervisors
Available from: 2013-11-06 Created: 2013-10-29 Last updated: 2013-11-06Bibliographically approved
2. Perturbed discrete time stochastic models
Open this publication in new window or tab >>Perturbed discrete time stochastic models
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, nonlinearly perturbed stochastic models in discrete time are considered. We give algorithms for construction of asymptotic expansions with respect to the perturbation parameter for various quantities of interest. In particular, asymptotic expansions are given for solutions of renewal equations, quasi-stationary distributions for semi-Markov processes, and ruin probabilities for risk processes.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2016. 48 p.
Keyword
Renewal equation, Perturbation, Asymptotic expansion, Regenerative process, Risk process, Semi-Markov process, Markov chain, Quasi-stationary distribution, Ruin probability, First hitting time, Solidarity property
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-128979 (URN)978-91-7649-422-6 (ISBN)
Public defence
2016-06-02, Sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript.

Available from: 2016-05-10 Created: 2016-04-11 Last updated: 2017-11-14Bibliographically approved

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Citation style
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