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Type: Journal article
Title: Insurance claims modulated by a hidden Brownian marked point process
Author: Elliott, R.
Chen, Z.
Duan, Q.
Citation: Insurance: Mathematics and Economics, 2009; 45(2):163-172
Publisher: Elsevier Science BV
Issue Date: 2009
ISSN: 0167-6687
Statement of
Robert J. Elliott, Zhiping Chen and Qihong Duan
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
Description: Copyright © 2009 Elsevier B.V. All rights reserved.
DOI: 10.1016/j.insmatheco.2009.05.008
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