Pricing of Risk in Accordance with the Pareto Distribution

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  • Ogura Hiroyuki
    Graduate School of Innovation Management, Tokyo Institute of Technology Japan Management Actuarial Consulting, Co., Ltd.

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  • パレート分布に従うリスクの経済合理性のある価格付けについて

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Pareto distribution is seen everywhere in natural and economic phenomena. Nevertheless, Pareto distribution does not always have expected value. If actual claim data derives such Pareto distribution, actuaries have a lot of difficulty in evaluating premium. For example, provided that power degree of generalized Pareto distribution is smaller than 2 and larger than 1, the average value of the random variable cannot be evaluated directly without upper and lower limit. However, with some measure transformation we can calculate expected value. Moreover it is shown that the method of calculation is suitable to the natural extension of the general economic premium principle treated by Hans Bühlmann in 1980 and 1984. The numerical example of this calculation is introduced using the data on the seismic hazard map which is provided by National Research Institute for Earth Science and Disaster Prevention.

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