The unbayesed credibility procedure proposed by Gerber is revisited. Its performance is discussed, connections are drawn to earlier literature, and some possible ideas of generalizations are investigated (and found fruitless).

This paper considers the bootstrapping approach for measuring reserve uncertainty when applying the model of Schnieper for reserves which separate Incurred But Not Reported (IBNR) and Incurred But Not Enough Reserved (IBNER) claims. The Schnieper method has been explored in Liu and Verrall (2009), and the Mean Square Errors of Prediction (MSEP) derived. This paper takes this further by deriving the full predictive distribution, using bootstrapping. Numerical examples are provided and the MSEP from the bootstrapping approach are compared with those obtained analytically.

In Industrial Fire insurance an aggregate limit for the amount retained by the policyholder under a deductible policy has been agreed upon more frequently in recent times. This agreement is equivalent to a stop-loss cover on the retained loss amount. For the Poisson-lognormal model the corresponding stop-loss net premium is calculated using various methods (normal power, translated gamma, various discretisations) and the methods are compared. Finally, the influence of the model parameters is examined and it is demonstrated how a variety of parameter value combinations can be reduced to only a few rating curves.

In order to make this report clear to those without experience in insurance matters, we first present some basic facts about the insurance business. In so doing we intentionally omit certain facts irrelevant to the present study. The most important omission of this kind is our assumption that the insurance business operates without administrative expenses and without sales costs. We also assume that the insurance business is run in such a way that no profit is made. It will be evident to readers already directly connected with insurance problems what further omissions we have made and why we have made them.

Insurance is the establishment of a contract between the insurance company and the insured person This contract is by tradition called the “insurance policy” and the insured person is called the “policyholder”. By agreeing to the insurance policy, the policyholder commits himself to paying certain premiums to the insurance company, and the insurance company commits itself to paying certain amounts to the policyholders. The conditions under which such payments are to be made are of many different kinds: the policy-holder dies, the policyholder becomes ill, a homeowner's house is burnt down, or the policyholder has a collision in his car. The circumstances under which a payment is to be made to the policy-holder are described in detail in the insurance policy. The amount to be paid is either fixed or variable: in life insurance the amount to be paid is always fixed and stated in the insurance policy, but in most other forms of insurance the intention is that the insurance compensate the policyholder for the losses he might incur as a consequence of the events covered by his policy.

This paper studies optimal defined-contribution (DC) pension management under stochastic interest rates and expected inflation. In addition to financial risk, we consider the risk of pre-retirement death and introduce life insurance to the pension account as an option to manage this risk. We formulate this pension management problem as a random horizon utility maximization problem and derive its explicit solution under the assumption of constant relative risk aversion utility. We calibrate our model to the U.S. data and demonstrate that the pension member’s demand for life insurance has a hump-shaped pattern with age and a U-shaped pattern with the real interest rate and expected inflation. The optimal pension account balance in our model resembles a variable annuity, wherein the death benefits are endogenously determined and depend on various factors including age, mortality, account balance, future contributions, preferences, and market conditions. Our study suggests that offering variable annuities with more flexible death benefits within the DC account could better cater to the bequest demands of its members.

Le calcul de la prime de l'assurance Incendie des bâtiments se trouve compliqué par le fait qu'il doit tenir compte, non seulement du bâtiment assuré, mais également des immeubles voisins.

Si deux bâtiments sont suffisamment éloignés, le risque qu'un incendie se propage de l'un à l'autre est minime, mais le risque de contiguïté, et par conséquent d'incendie total, est d'autant plus grand que leur distance est plus faible.

La mesure dans laquelle le risque de contiguïté doit être retenu pour la tarification est un des problèmes les plus importants que l'Actuaire a à résoudre en assurance Incendie.

Pour qu'un incendie puisse s'étendre à d'autres bâtiments, le feu doit embrasser d'abord les éléments extérieurs du bâtiment assuré, c'est-à-dire les murs, la cheminée, la toiture ou les constructions en bois attenantes. Nous appellerons de tels incendies: incendies extérieurs par opposition à incendies intérieurs qui n'embrassent que le contenu du bâtiment et les aménagements intérieurs.

Par risque propre d'un bâtiment nous entendons l'indemnité moyenne annuelle de sinistre, sous la condition que ce bâtiment ne soit pas exposé au risque de contiguïté d'autres immeubles.

Le risque propre se divise en une fraction qui concerne les incendies intérieurs et une autre fraction concernant les incendies extérieurs,

Le deuxième terme Re peut être exprimé par le produit de la probabilité d'un incendie extérieur et de l'indemnité moyenne de cet incendie, soit

Les éléments de ce risque propre peuvent être observés pour différents groupes de risques, c'est-à-dire chaque groupe comprenant des bâtiments d'un même genre, par exemple en ce qui concerne leur construction, leur dimension ou leur destination.

In his paper “Actuarial Activity in General Insurance in the Northern Countries of Europe” L. Wilhelmsen gives amongst other things an account of the work carried on by Centralstället för nordisk ömsesidig Brandförsäkringsstatistik (CNÖB, the Northern Central Office for Fire Insurance Statistics from Mutual Companies). In this he states that one part of the organisation's work is the carrying out of special investigations of current problems with material collected on each occasion for the purpose.

The object of this paper is to report investigations carried out in CNÖB on the connection between temperature and risk premium in fire insurance. The material used is made up exclusively of civil risks (buildings) and the material has been taken from Sweden and Norway. The background to the investigation consists in the fact that in Scandinavia the risk premiums for fire insurance show an apparent geographical variation, in that the amount clearly increases in the most northerly provinces.

As we know that the fire damage directly or indirectly caused by heating systems (chimney fires, cracked building blocks, embers from fireplaces or chimneys etc.) represents a large proportion of the damage in civil risks (40-50%, in some materials 60% or more), that the proportion is greatest in the northern parts and that in the Swedish material about 50% of the damage in any one area falls in the four months December to March, it is quite reasonable to trace the influence of the temperature factor behind the geographical variation; the colder the climate, the more lighting of fires and the more damage. This line of argument is connected exclusively to the frequency of damage; we shall return later to the mean degree of damage.

Cette note est présentée par un actuaire qui n'a eu que depuis peu à s'intéresser aux branches d'assurances autres que la Vie et seulement du point de vue de la gestion administrative, à l'occasion de la mise en œuvre d'un grand ensemble électronique de traitement de l'information. Il ne faut done pas s'attendre à trouver ici une théorie sur la détermination des montants à réserver pour les sinistres à régler, encore moins sur la construction des tarifs d'assurance automobile.

Néanmoins, la gestion administrative n'ayant pas pour seul but de recueillir et de classer des données comptables, nous serons bien naturellement conduits à prévoir comment ces données peuvent être liées à des recherches sur ces deux questions fondamentales.