Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory

Good estimates for the tails of loss severity distributions are essential for pricing or positioning high-excess loss layers in reinsurance. We describe parametric curve-fitting methods for modelling extreme historical losses. These methods revolve around the generalized Pareto distribution and are supported by extreme value theory. We summarize relevant theoretical results and provide an extensive example of their application to Danish data on large fire insurance losse

Magnetic Anomaly Absolute Positioning for Hypersonic Aircraft

GPS has proven to be an extremely valuable asset for navigation, and timing. GPS has become the standard navigation system for all applications, but GPS has limitations. GPS is susceptible to jamming, spoofing, and in the case of hypersonic aircraft, is likely unavailable. When an aircraft is traveling at hypersonic speeds, there is a plasma sheath that surrounds the aircraft. This plasma sheath blocks electromagnetic waves, and is therefore responsible for a GPS blackout. GPS unavailability for hypersonic aircraft has prompted the research into the viability of alternate navigation systems for these aircraft. This paper seeks to explore the viability of MagNav for hypersonic aircraft. Hypersonic aircraft present new challenges for MagNav including: high altitudes, high speeds, large scale map availability, and new noise sources. This paper explores these challenges to determine if any poses an insurmountable problem. Simulations are conducted to explore the potential performance of MagNav on a hypersonic vehicle. These simulations conclude that MagNav is viable on a hypersonic aircraft

Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling

The idea of using common Poisson shock processes to model dependent event frequencies is well known in the reliability literature. In this paper we examine these models in the context of insurance loss modelling and credit risk modelling. To do this we set up a very general common shock framework for losses of a number of different types that allows for both dependence in loss frequencies across types and dependence in loss severities. Our aims are threefold: to demonstrate that the common shock model is a very natural way of approaching the modelling of dependent losses in an insurance or risk management context; to provide a summary of some analytical results concerning the nature of the dependence implied by the common shock specification; to examine the aggregate loss distribution that results from the model and its sensitivity to the specification of the model parameter

Time series copula models using d-vines and v-transforms

An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically inverting v-transforms, models are constructed that can describe both stochastic volatility in the magnitude of price movements and serial correlation in their directions. In combination with parametric marginal distributions it is shown that these models can rival and sometimes outperform well-known models in the extended GARCH family

Multivariate Archimedean copulas, dd-monotone functions and ℓ1\ell_1-norm symmetric distributions

It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a $d$-dimensional copula is that the generator is a $d$-monotone function. The class of $d$-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of $d$-dimensional $\ell_1$-norm symmetric distributions that place no point mass at the origin. The $d$-monotone Archimedean copula generators may be characterized using a little-known integral transform of Williamson [Duke Math. J. 23 (1956) 189--207] in an analogous manner to the well-known Bernstein--Widder characterization of completely monotone generators in terms of the Laplace transform. These insights allow the construction of new Archimedean copula families and provide a general solution to the problem of sampling multivariate Archimedean copulas. They also yield useful expressions for the $d$-dimensional Kendall function and Kendall's rank correlation coefficients and facilitate the derivation of results on the existence of densities and the description of singular components for Archimedean copulas. The existence of a sharp lower bound for Archimedean copulas with respect to the positive lower orthant dependence ordering is shown.Comment: Published in at http://dx.doi.org/10.1214/07-AOS556 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org