Insurance claims modulated by a hidden marked point process

Robert J. Elliott; Tak Kuen Siu; Hailiang Yang

doi:10.1109/ACC.2007.4283152

Insurance claims modulated by a hidden marked point process

Robert J. Elliott, Tak Kuen Siu, Hailiang Yang

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

5 Citations (Scopus)

31 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 language	English
Title of host publication	Proceedings of the 2007 American Control Conference, ACC
Place of Publication	New York
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	390-395
Number of pages	6
ISBN (Print)	1424409888, 9781424409884
DOIs	https://doi.org/10.1109/ACC.2007.4283152
Publication status	Published - 2007
Externally published	Yes
Event	2007 American Control Conference, ACC - New York, NY, United States Duration: 9 Jul 2007 → 13 Jul 2007

Other

Other	2007 American Control Conference, ACC
Country/Territory	United States
City	New York, NY
Period	9/07/07 → 13/07/07

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 Universityâ€™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 [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

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Cite this

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title = "Insurance claims modulated by a hidden marked point process",

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.",

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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{\^a}€{\texttrademark}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 [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.; 2007 American Control Conference, ACC ; Conference date: 09-07-2007 Through 13-07-2007",

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Insurance claims modulated by a hidden marked point process. / Elliott, Robert J.; Siu, Tak Kuen; Yang, Hailiang.
Proceedings of the 2007 American Control Conference, ACC. New York: Institute of Electrical and Electronics Engineers (IEEE), 2007. p. 390-395 4283152.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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N1 - 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 Universityâ€™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 [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

PY - 2007

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N2 - 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.

AB - 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.

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Insurance claims modulated by a hidden marked point process

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