长尾业务对非寿险公司的冲击与防范

近年来，在国际保险市场上大量的非寿险公司因承保长尾业务而导致破产倒闭。同时不少国际再保险巨头因分入长尾业务而面临巨大的偿付压力。对于长尾业务所计提的准备金的充足率已经成为影响非寿险公司评级的重要标志。文章探讨了长尾业务的概念，分析了长尾业务的成因，介绍了国际上长尾业务的防范方法，对我国的非寿险公司防范长尾业务具有一定的借鉴作用。     

Separation of small and large claims on the basis of collective models

This paper is inspired by two papers of Riegel who proposed to consider the paid and incurred loss development of the individual claims and to use a filter in order to separate small and large claims and to construct loss development squares for the paid or incurred small or large claims and for the numbers of large claims. We show that such loss development squares can be constructed from collective models for the accident years. Moreover, under certain assumptions on these collective models, we show that a development pattern exists for each of these loss development squares, which implies that various methods of loss reserving can be used for prediction and that the chain ladder method is a natural method for the prediction of future numbers of large claims.     

A model study about the applicability of the Chain Ladder method

Loss Reserving is a major topic of actuarial sciences with a long tradition and well-established methods – both in science and in practice. With the implementation of Solvency II, stochastic methods and modelling the stochastic behaviour of individual claim portfolios will receive additional attention. The author has recently proposed a three-dimensional (3D) stochastic model of claim development. It models a reasonable claim process from first principle by integrating realistic processes of claim occurrence, claim reporting and claim settlement. This paper investigates the ability of the Chain Ladder (CL) method to adequately forecast outstanding claims within the framework of the 3D model. This allows one to find conditions under which the CL method is adequate for outstanding claim prediction, and others in which it fails. Monte Carlo (MC) simulations are performed, lending support to the theoretic results. The analysis leads to additional suggestions concerning the use of the CL method.     

Bifurcation of attritional and large losses in an additive IBNR environment

In certain segments, IBNR calculations on paid triangles are more stable than on incurred triangles. However, calculations on payments often do not adequately take large losses into account. An IBNR method which separates large and attritional losses and thus allows to use payments for the attritional and incurred amounts for the large losses has been introduced by Riegel (see Riegel, U. (2014). A bifurcation approach for attritional and large losses in chain ladder calculations. Astin Bulletin 44, 127–172). The method corresponds to a stochastic model that is based on Mack’s chain ladder model. In this paper, we analyse a quasi-additive version of this model, i.e. a version which is in essence based on the assumptions of the additive (or incremental loss ratio) method. We describe the corresponding IBNR method and derive formulas for the mean squared error of prediction.     

On the distribution of discounted loss reserves using generalized linear models

Renshaw and Verrall [] specified the generalized linear model (GLM) underlying the chain-ladder technique and suggested some other GLMs which might be useful in claims reserving. The purpose of this paper is to construct bounds for the discounted loss reserve within the framework of GLMs. Exact calculation of the distribution of the total reserve is not feasible, and hence the determination of lower and upper bounds with a simpler structure is a possible way out. The paper ends with numerical examples illustrating the usefulness of the presented approximations.     

Limiting Distribution of the Studentized Largest Observation1

Abstract

The distribution of the “studentized” largest observation, i.e. the largest observation minus the sample mean divided by the sample standard deviation, is fundamental in the theory of rejection of outlying observations. For samples up to size 25 from a normal population, this distribution has been tabulated by Grubbs [5]. The object of the present work is to derive the limiting distribution of the studentized largest observation for a general population. Empirical observations of Gumbel seem to indicate that if the largest observation has a limiting distribution, then the studentized largest observation has the same one [6]. Here this will be shown to hold under general conditions. This solves the problem raised by Borenius [1, p. 151].