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Insurance claims modulated by a hidden Brownian marked point process

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  • Elliott, Robert J.
  • Chen, Zhiping
  • Duan, Qihong

Abstract

Aimed at better modeling insurance claims in an economic environment driven by business cycles, a new Markov-modulated Poisson process model is proposed, and an algorithm is derived to estimate the hidden Markov process by using the observed information. Our method differs from existing ones in the following ways: the new hidden process can model more efficiently the cyclic state of the economic environment; our theory is based on a variation of the law of large numbers and is easy to understand; the Fourier expansion-based parameter estimation algorithm is flexible and can be more easily implemented than other algorithms. Simulation results not only demonstrate the practicality of our model and algorithm, but also show the efficiency and robustness of the estimation algorithm.

Suggested Citation

  • Elliott, Robert J. & Chen, Zhiping & Duan, Qihong, 2009. "Insurance claims modulated by a hidden Brownian marked point process," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 163-172, October.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:2:p:163-172
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    References listed on IDEAS

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    Cited by:

    1. Qihong Duan & Junrong Liu, 2015. "A first step to implement Gillespie’s algorithm with rejection sampling," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 85-95, March.
    2. Duan, Qihong & Wei, Ying & Chen, Zhiping, 2014. "Relationship between the benchmark interest rate and a macroeconomic indicator," Economic Modelling, Elsevier, vol. 38(C), pages 220-226.

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