Insurance claims modulated by a hidden Brownian marked point process

Robert J. Elliott, Zhiping Chen and Qihong Duan

Insurance: Mathematics and Economics, 2009, vol. 45, issue 2, 163-172

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.

Keywords: Insurance; risk; models; Markov-modulated; Poisson; processes; Brownian; motion; Reference; probability (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:45:y:2009:i:2:p:163-172

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