Bivariate hidden Markov model to capture the dependency in claim estimate

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, İstatistik Bölümü, Türkiye

Tezin Onay Tarihi: 2016

Öğrenci: ZARINA OFLAZ

Eş Danışman: SEVTAP AYŞE KESTEL, CEYLAN YOZGATLIGİL

Özet:

Most actuarial models rely on an assumption that both claim counts and aggregate claim amounts are serially independent, that simplifies the study of many risk quantities. However, this hypothesis does not always reflect the reality and is too restrictive in different frameworks. Some weather or economic conditions reasonably affect the claim-causing events, as a result, it influences both the claim number and the claim amount distributions. The unobservable background factor can be characterized by a hidden finite state Markov chain. In our study, we propose a novel approach for modeling claim dependence, Bivariate Hidden Markov Model (BHMM), which to our knowledge has not been studied before. We assume that the claim counts and the aggregate claim amounts are mutually dependent 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. To fit the model EM algorithm is used. In order to maximize the state-dependent part of complete-data log-likelihood of bivariate HMMs, we established and proved three propositions. In application part of our thesis, we fit the Poisson-Normal HMM with a different number of states to vehicle insurance observations for Istanbul taken from Traffic Insurances Information and Monitoring Center (TRAMER) for the years 2007-2009. In addition, we performed forecasting of distributions and state prediction, obtained the most likely sequence of states.