Estimation of the parameters of a Markov-modulated loss process in insurance

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• 作者：Armelle Guillou ; St¨¦phane Loisel ; Gilles Stupfler
• 关键词：Markov-modulated Poisson process ; Maximum likelihood estimator ; Strong consistency ; EM algorithm
• 刊名：Insurance: Mathematics and Economics
• 出版年：2013
• 出版时间：September, 2013
• 年：2013
• 卷：53
• 期：2
• 页码：388-404
• 全文大小：677 K

文摘

We present a new model of loss processes in insurance. The process is a couple where is a univariate Markov-modulated Poisson process (MMPP) and is a multivariate loss process whose behavior is driven by . We prove the strong consistency of the maximum likelihood estimator of the parameters of this model and present an EM algorithm to compute it in practice. The method is illustrated with simulations and real sets of insurance data.