Jan Dhaene

A robustification of the chain-ladder method

Abstract In a non-life insurance business an insurer often needs to build up a reserve to able to meet his or her future obligations arising from incurred but not reported completely claims. To forecast these claims reserves, a simple but generally accepted algorithm is the classical chain-ladder method. Recent research essentially focused on the underlying model for the claims reserves to come to appropriate bounds for the estimates of future claims reserves. Our research concentrates on scenarios with outlying data. On closer examination it is demonstrated that the forecasts for future claims reserves are very dependent on outlying observations. The paper focuses on two approaches to robustify the chain-ladder method: the first method detects and adjusts the outlying values, whereas the second method is based on a robust generalized linear model technique. In this way insurers will be able to find a reserve that is similar to the reserve they would have found if the data contained no outliers. Because the robust method flags the outliers, it is possible to examine these observations for further examination. For obtaining the corresponding standard errors the bootstrapping technique is applied. The robust chain-ladder method is applied to several run-off triangles with and without outliers, showing its excellent performance.

“Self-Annuitization and Ruin in Retirement”, Moshe Arye Milevsky and Chris Robinson, October 2000

JAN DHAENE,* MARC J. GOOVAERTS, AND ROB KAAS The present paper is a very interesting one because it introduces financial modeling into classical actuarial problems in a way that is both very nice and relatively easy to grasp. The paper derives an approximation to the distribution of Asian options and formulates very nicely the connection with the idea behind ruin probabilities in case interest is described by a Wiener process. The results obtained are attractive because, to some extent, they demystify the stochastic discount process. While Wiener measures should be familiar tools to actuaries certifying the accounts of financial conglomerates, one such actuary wasn’t ashamed to state that he only knew about the Wiener Sängerknaben. One of the merits of this paper is that it introduces a Wiener measure into a mortality model with stochastic interest returns. In addition, the mathematically equivalent problem of pricing Asian options is tackled. Deriving approximations for net present values under stochastic return models is necessary because the known analytical distributions for problems of this kind are scarce and difficult to apply in practice. To determine the distribution of a stochastic annuity (nonstochastic mortality but random return) is an old mathematical problem, totally equivalent to the so-called Callogero model of mathematical physics, which was solved in the early 1970s. Attempts to generalize the results have been unsuccessful in mathematical physics for about 30 years. To indicate the importance of having approximations to this very important actuarial problem, the interested reader is referred to De Schepper et al. (1994), formula (3.1) which provides us with the distribution density of a stochastic annuity: