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Hybrid Hidden Markov Model and Generalized Linear Model for Auto Insurance Premiums

Title:

Hybrid Hidden Markov Model and Generalized Linear Model for Auto Insurance Premiums

Berry, Lucas (2016) Hybrid Hidden Markov Model and Generalized Linear Model for Auto Insurance Premiums. Masters thesis, Concordia University.

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Abstract

We describe a new approach to estimate the pure premium for automobile insurance. Using the theory of hidden Markov models (HMM) we derive a Poisson-gamma HMM and a hybrid between HMMs and generalized linear models (HMM-GLM). The hidden state is meant to represent a driver's skill thus capturing an unseen variable. The Poisson-gamma HMM and HMM-GLM have two emissions, severity and claim count, making it easier to compare to current actuarial models. The proposed models help deal with the overdispersion problem in claim counts and introduces dependence between the severity and claim count. We derive maximum likelihood estimates for the parameters of the proposed models and then using simulations with the Expectation Maximization algorithm we compare the three methods: GLMs, HMMs and HMM-GLMs. We show that in some instances the HMM-GLM outperforms the standard GLM, while the Poisson-gamma HMM under-performs the other models. Thus in certain situations it may be worth the added complexity of a HMM-GLM.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Berry, Lucas
Institution:Concordia University
Degree Name:M.A.
Program:Mathematics
Date:9 December 2016
Thesis Supervisor(s):Garrido, Jose and Mailhot, Melina
ID Code:982074
Deposited By: LUCAS BERRY
Deposited On:07 Jun 2017 17:36
Last Modified:18 Jan 2018 17:54
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