Bayesian Inference of a Mixture Model with Extreme Value Distributions in Korean Medical Insurance Applications

Jae Hoon Jho; 이근창

Journal of Insurance and Finance

2013, 24(2), pp.71-98
Publisher : Korea Insurance Research Institute
Research Area : Business Management

Jae Hoon Jho ¹ , 이근창 ²

¹ 영남대학교
² 영남대학교

ABSTRACT

In this paper, we introduce a practical method of estimating the threshold over which a heavy-tailed distribution is approximated asymptotically for the underlying distribution of extreme events. We introduce a mixture model of a loss distribution of a certain parametric form below a threshold and a heavy-tailed distribution above the threshold. The number of exceedances over a threshold are considered a random variable for a prior distribution in the Bayesian framework in order to estimate the threshold and corresponding extreme value index. A numerical example is given to illustrate the Bayesian estimation of the parameters by applying the mixture model to losses in medical insurance policies in Korea. About a 10.5% extra charge over traditionally calculated premiums seems necessary to hedge the risk embedded in the heavy-tailed loss distribution.
KEYWORDS

Bayesian estimation , distribution , extreme value distributions , extreme value theory , generalized Pareto mixture distribution , Korean medical insurance , Metropolis-Hastings , threshold
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KCI Citation (6)

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