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Workshops & seminars

MSc thesis defence in Mathematics

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


Date & time
Friday, December 9, 2016
1:30 p.m. – 3:30 p.m.
Cost

This event is free

Contact

Marie-France Leclere
Ext. 3250

Where

J.W. McConnell Building
1400 De Maisonneuve W.
Room 921-4

Wheel chair accessible

Yes

Speaker: Mr. Lucas Berry (MA)

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 over dispersion 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.

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