AGGREGATE CLAIM ESTIMATION USING BIVARIATE HIDDEN MARKOV MODEL
Oflaz, Zarina Nukeshtayeva and Yozgatligil, Ceylan and Selcuk-Kestel, A.
Sevtap
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Abstract
In this paper, we propose an approach for modeling claim dependence,
with the assumption that the claim numbers and the aggregate claim
amounts are mutually and serially dependent through an underlying hidden
state and can be characterized by a hidden finite state Markov chain
using bivariate Hidden Markov Model (BHMM). We construct three different
BHMMs, namely Poisson-Normal HMM, Poisson-Gamma HMM, and Negative
Binomial- Gamma HMM, stemming from the most commonly used distributions
in insurancce studies. Expectation Maximization algorithm is implemented
and for the maximization of the state-dependent part of log-likelihood
of BHMMs, the estimates are derived analytically. To illustrate the
proposed model, motor third-party liability claims in Istanbul, Turkey,
are employed in the frame of Poisson-Normal HMM under a different number
of states. In addition, we derive the forecast distribution, calculate
state predictions, and determine the most likely sequence of states. The
results indicate that the dependence under indirect factors can be
captured in terms of different states, namely low, medium, and high
states.... Show more Show less