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Analytical studies in stop-loss reinsurance. II
Authors:S Vajda
Institution:Epsom , Surrey
Abstract:Abstract

I

In an earlier paper 5] we discussed the problem of finding an unbiased estimator of  id= where p (x, 0) is a given frequency density and 0 is a (set of) parameter(s). In general,  id= will not be an unbiased estimator of (1), when Ô is an unbiased estimate of O. In 5] it was shown that  /></span> is an unbiased estimator of (1), if we define <i>y<sub>i</sub> </i>, as the larger of 0 and <i>X</i> <sub>j</sub> - <i>c</i>. It was emphasized that the resulting estimate may very well be zero, even when it is unreasonable to assume that the premium for a stop.loss reinsurance. defined by a frequency <i>p</i> (<i>x, 0</i>) of claims <i>x</i> and <i>a</i> critical limit <i>c</i>, should be zero when the critical limit has not been exceeded during the <i>n</i> years considered for the determination of the premium.</td>
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