For reinsurance contract simulated annual losses, an inequality relating their standard deviation and mean is found, σ f ≥ m f μ A C μ 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.
Part of the book: Accounting from a Cross-Cultural Perspective
Propose use kurtosis divided by skewness squared as shape factor, and use the global or conditional minimum/maximum of this shape factor for selecting and differentiating distribution families. Semi-empirical formulas for that lower/upper bound are calculated for various distribution families, with the aid of Computer Algebra System, for fitting hard to match distributions. Previous studies show high CV distribution is hard to fit and simulate, this study extends that conclusion to cases with low CV but still hard to match EP curves, characterized by having shape factors close to 1. The maximal likelihood approach of distribution fit can tell us which distribution family is better suited for an empirical distribution, but the shape factor range information can tell us why a distribution cannot fit well, or is not suitable at all. So the shape factor, in a sense, determines the EP curve shape.
Part of the book: Applied Mathematics