Estimation of claim amounts using bivariate hidden Markov models

Estimation of claim amounts using bivariate hidden Markov models

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Speaker(s): A. Sevtap Kestel (Middle East Technical University (METU))

Most actuarial models rely on an assumption that both claim counts and aggregate claim amounts are independent which does not always reflect the reality and is too restrictive in different frameworks. Some conditions such as weather, economical or financial factors affect the claim-causing events, consequently, the claim number and the claim amount behaviors. These unidentifiable background factors are aimed to be characterized by a hidden finite state Markov chain. In this study, we propose an approach for modeling the claim dependence by employing Bivariate Hidden Markov Model (BHMM), under the assumption that the claim counts and the aggregate claim amounts are mutually and serially dependent through an underlying hidden state. We construct three different Bivariate Hidden Markov Models, namely Poisson-Normal HMM, Poisson-Gamma HMM and Negative Binomial-Gamma HMM at which EM algorithm is used to fit the models. In order to maximize the state-dependent part of complete-observations, we establish and prove these the log-likelihoods of bivariate HMMs. As an illustration, we employ the Poisson-Normal HMM with a different number of states to the automobile insurance claims taken from Turkey. In addition, we also perform forecasting and state predictions based on the most likely sequence of states.

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