Based On Extreme Value Theory Of Non-life Insurance Actuarial Study

In this paper, a new method of non-life actuary with extremely large loss has beenpresented by employing the extreme value theory. This paper not only base on a lot ofresearches in classic non-life insurance but also take a full advantage of the extremevalue theory which has a number of fine properties. When referred to extreme valuetheory and the peaks over threshold model, what we concern is just the tail of thedistribution, not the whole distribution, there is no double that this can avoid handlingthe very complicated problem of which distribution the underlying dataset belongs,what's more, the high quantile can be calculated with great precision and this is veryimportant to the insurance company. In the GPD modeling process, first, the test ofextreme value condition has been introduced, and then different methods of optimalchoice of the threshold were given. Then we fit the extremely large loss data to ageneralized pareto distribution with different estimate methods, including themaximum likelihood estimate,Hill semi-parameter estimate and moment estimate ect,After the generalized pareto distribution have been built, a non-parameter method oftest have been given to validate the GPD model, then Under the hypothesis ofcompound Poisson distribution, a new method of calculation the pure premium ofExecss-of-Loss insurance was given.