An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

Frank Xuyan Wang

A chapter in Accounting from a Cross-Cultural Perspective from IntechOpen

Abstract: For reinsurance contract simulated annual losses, an inequality relating their standard deviation and mean is found, ? f >= m f ? A C ? A , where the coefficient in the inequality is the square root of the ratio of numbers of zero losses years to numbers of non-zero losses years. The largest such coefficient is also proved to be the universal upper bound. As direct application of this inequality, bounds for other risk measures of reinsurance contract, the TVaR (average of the annual losses that are larger than a given loss), the probability of attaching (greater than a given attachment loss), and the probability of exceeding (the annual loss limit) are obtained, which in turn reveal the capability upper limit of the simulation approach.

Keywords: reinsurance contract; simulation; standard deviation; coefficient of variation; inequality; ratio distribution; model risk (search for similar items in EconPapers)
JEL-codes: M41 (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:140081

DOI: 10.5772/intechopen.76265

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