Insurance claims modulated by a hidden marked point process

Robert J. Elliott, Tak Kuen Siu, Hailiang Yang

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

2 Citations (Scopus)
7 Downloads (Pure)

Abstract

Recently Markov-modulated compound Poisson models have gained its popularity in modelling insurance claims in the actuarial science literature. A Markov-modulated compound Poisson model can provide a realistic and flexibile way to model aggregate insurance claims by incorporating the impact of hidden states of an economy on claim frequencies and claim sizes. However, in practice, the Markov chain in the model is not observable. It is of practical interest to develop some methods to estimate the hidden state of the Markov chain and other unknown model parameters of the Markov-modulated compound Poisson model. This paper considers this important issue. We shall develop filters and smoothers for the hidden state of the economy underlying the Markov-modulated compound Poisson model. In general, we consider the case when both the stochastic intensity and the distribution of the claim sizes of the compound Poisson process depend on the hidden Markov chain. The filter and smoother provide an optimal way to estimate the insurance claims model in the "mean-squared- error" sense. We shall also develop estimators for the unknown model parameters of the Markov-modulated marked point process using the robust filter-based and smoother-based EM algorithms.

Original languageEnglish
Title of host publicationProceedings of the 2007 American Control Conference, ACC
Place of PublicationNew York
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages390-395
Number of pages6
ISBN (Print)1424409888, 9781424409884
DOIs
Publication statusPublished - 2007
Externally publishedYes
Event2007 American Control Conference, ACC - New York, NY, United States
Duration: 9 Jul 200713 Jul 2007

Other

Other2007 American Control Conference, ACC
CountryUnited States
CityNew York, NY
Period9/07/0713/07/07

Bibliographical note

Copyright 2007 IEEE. Reprinted from Proceedings of the 2007 American Control Conference. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Macquarie University’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

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