bluuebunny/crossref_metadata_2025_split huggingface dataset:
Earthquakes and Windstorm — Natural Disasters
Authors: Ryder J. M. , Kimber D. J. 
Published: July 2016

Earthquakes and Windstorm can range in size from small easily insurable instances up to full scale Natural Disasters. This note is particularly concerned with the problem of forecasting, rating and insuring earthquakes and windstorm at the natural disaster end of this scale.Before we tackle the peculiar problems of natural disaster insurance it is worth having a look at why insurance works so well in practice.Is it because actuaries and statisticians have precisely measured the statistical risks involved, and have developed a detailed and complex mathematical approach to insurance, a true “Technical Basis” for Insurance? Or is it really quite simple?A quotation (the first of many) from R. Heller [1] is relevant.“The great and fabled business empires with hardly an exception were built… on irresistable ideas of elemental simplicity.”Insurance is one of these great empires, and some of the simple ideas which may explain why insurance works so well are suggested below.
The Efficiency of a Bonus-Malus System
Authors: De Pril Nelson 
Published: July 2016

AbstractThe concept efficiency of a bonus-mains system was defined, apparently in a totally different way, consecutively by Loimaranta (1972) and Lemaire (1975, 1976). In this paper we start with a more general model that leads us to a definition of efficiency that contains both earlier ones as special cases. Further we introduce the definition of efficiency over a finite planning horizon and consider the efficiency not only for a single risk but also for the entire risk group. As a consequence of our approach we can also generalize the concepts excess premium and central value as they were introduced by Loimaranta.
Contribution à l'étude du coût des sinistres automobiles
Authors: Picard P. 
Published: July 2016

SummaryAfter having a look at the results obtained by adjustment of automobile claims amounts distribution, we research how the number and the time-configuration of past claims condition the claims law of probability.We have statistics about a group of 471 000 cars which was followed for three years: 1970, 1971 and 1972. We use mathematical technics and among multi-dimensional analysis, we use factorial analysis of correspondance (A.F.C.). A.F.C. permits us to show the link which exists between the claim amount of the third year and the number of claims during the two years before. A quantitative analysis of the corporal claims shows that, of the frequency of corporal claims during the third year growths up in function of the number of past claims, the expected corporal claims amount of the third year decreases as the square of the material claims number during the two first years.
Probability of Ruin under Inflationary Conditions or under Experience Rating
Authors: Taylor G. C. 
Published: July 2016

The effect of inflation of premium income and claims size distribution, but not of free reserves, on the probability of ruin of an insurer is studied.An interesting similarity between this problem and the ruin problem in an experience-rated scheme is exhibited. This similarity allows the deduction of parallel results for the two problems in later sections.It is shown that the probability of ruin is always increased when the (constant) inflation rate is increased.The distribution of aggregate claims under inflationary conditions is described and used to calculate an upper bound on the ruin probability. Some numerical examples show that this bound is not always sharp enough to be practically useful. It is also shown, however, that this bound can be used to construct an approximation of the effect of inflation on ruin probability.It is shown that if inflation occurs at a constant rate, then ruin is certain, irrespective of the smallness of that rate and of the largeness of initial free reserves and the safety margin in the premium. The corresponding result for experiencerated schemes is that a practical and “intuitively reasonable” experience-rating scheme leads eventually to certain ruin.Finally, a simple modification of the techniques of the paper is made in order to bring investment income into account.
The Theory of Insurance Risk Premiums—A Re-Examination in the Light of Recent Developments in Capital Market Theory
Authors: Kahane Yehuda 
Published: July 2016

The premium calculation principle is one of the main objectives of study for actuaries. There seems to be full agreement among the leading theoreticians in the field that the insurance premium should reflect both the expected claims and certain loadings. This is true for policy, risk or portfolio. There are three types of positive loadings: a) a loading to cover commissions, administrative costs and claim-settlement expenses; b) a loading to cover some profit (a cost-plus approach); and c) a loading for the risk taken by the insurer when underwriting the policy. The administrative costs can be considered a part of “expected gross claims”. Thus, the insurer's ratemaking decision depends on his ability to estimate expected claims (including costs) and on the selection of a fair risk loading.The main concern in the literature is the appropriate measurement of the risk and the exact loading formula. Bühlmann [1970, ch. 5] and others identified four possible principles of risk loading, namely, the expected value principle, the standard deviation loading, the variance loading, and the loading according to the principle of constant utility. Various studies point to the advantages and disadvantages of these principles and also examine some additional loading forms—semi-variance, skewness, etc. (e.g., Bühlmann [1970], Benktander [1971], Berger [1972], Burness [1972], Berliner [1974], Berliner and Benktander [1976], Bohman [1976], Cooper [1974], Gerber [1975] and others). Despite different preferences in choosing the appropriate loading calculation principle, all seem to agree that the risk loading must be positive, since, otherwise, the firm would just have to wait for its ruin, that is bound to come sooner or later, according to risk theory.The purpose of this article is to re-examine the appropriate principle of premium calculation in light of the recent developments in the theory of finance and especially in the theory of capital market equilibrium. These developments may suggest a new point of view and raise a few questions regarding the loading rules.
Finite Sum Evaluation of the Negative Binomial-Exponential Model
Authors: Panjer Harry H. , Willmot Gordon E. 
Published: July 2016

The compound negative binomial distribution with exponential claim amounts (severity) distribution is shown to be equivalent to a compound binomial distribution with exponential claim amounts (severity) with a different parameter. As a result of this, the distribution function and net stop-loss premiums for the Negative Binomial-Exponential model can be calculated exactly as finite sums if the negative binomial parameter α is a positive integer.The result is a generalization of Lundberg (1940).Consider the distribution ofwhere X1, X2, X3, … are independently and identically distributed random variables with common exponential distribution functionand N is an integer valued random variable with probability functionThen the distribution function of S is given byIf MX(t), MN(t) and MS(t) are the associated moment generating functions, then
Automobile Insurance: Canadian Accident-Free Classification System
Authors: Martin D. B. 
Published: July 2016

The precise wording of the heading is deliberate. The Canadian system is not a “bonus” nor is it properly described as “no claim”; it is a sub-classification of insureds according to whether they have been accident-free during a term of years ending at the inception of the insurance period. Specific rates are quoted in the Tariff for each sub-class, based broadly on the relative experiences; as a matter of arithmetical convenience, premium rates are calculated by applying discounts or surcharges to a “key” rate, but the percentage discounts or surcharges are not quoted in the Tariff, the Policy or the renewal papers.In the early 1930's a “no claim bonus” on British lines was part of the Canadian automobile insurance system. A percentage reduction or “bonus” was allowed from the premium specified in the Policy, provided the insured had owned and operated a private passenger car, free of accident or revocation of driving license, for a period of up to three years before the inception of the Policy. At that time the Automobile Insurance Market was profitable and highly competitive, both as between Companies and as between Agents. Because of inter-Company competition, confirmation of entitlement to the bonus was rarely attempted. Often it was not possible, as most Companies did not maintain an alphabetical index of insureds; an effort to set up an inter-Company claim-recording bureau broke down through sheer weight of numbers of claims.
Contribution a l'etude du bonus pour non sinistre en assurance automobile
Authors: Thyrion P. 
Published: July 2016

La sélection des risques est un des premiers principes fondamentaux que la théorie de l'assurance a dégagés. Il se traduit essentiellement par la répartition des risques en classes de tarif homogènes et il prémunit l'assureur contre le danger de voir „le mauvais risque chasser le bon”.Pour créer des classes de tarif homogènes, il faut théoriquement repérer tous les facteurs influençant le risque et en chiffrer l'effet. Si cela est fait, la fluctuation des résultats individuels autour de la moyenne n'est que l'effet accidentel du hasard et ne peut donner lieu a posteriori à rectification de la prime: il n'y a rien d'inéquitable à ce que les titulaires des contrats non sinistrés paient pour les autres puisque tous sont égaux devant le risque.Comme dans toute science appliquée, la mise en oeuvre des principes se heurte parfois à de grandes difficultés d'exécution. Dans la pratique il n'est généralement pas question de repérer tous les facteurs du risque, mais seulement les principaux, ne fût-ce qu'en raison de l'impossibilité de conduire des études statistiques valables sur une multitude de groupes peu étoffés. On ne peut donc faire grief au praticien d'estimer qu'il a créé des classes homogènes lorsque celles-ci tiennent compte des principaux facteurs de risque.Mais l'optique change si, pour l'une ou l'autre raison qu'il importe peu de préciser, le tarif néglige un ou des facteurs dont le bon sens et l'expérience — à défaut du calcul — prouvent l'influence appréciable.
On a class of measures of dispersion with application to optimal reinsurance
Authors: Ohlin Jan 
Published: July 2016

In this paper we will investigate the following reinsurance problem: An insurer, whose total claims for a certain period may be regarded as a random variable x with expected value Ex = m, wishes to cede part of his business to a reinsurer. A reinsurance treaty will consist of rule for the division of x between the two parties. For any observed value of x it should define uniquely what amount should be borne by the ceding insurer. The amount borne by the reinsurer is then simply the remaining part of x.We shall assume that the insurer has already decided how much of his business he wishes to cede, in the sense that he wants to retain a part of the total risk with expected value m — c, where c is a fixed constant, o < c < m.Using the terminology introduced by Kahn in (2) we will describe a reinsurance contract by a transformation (or function) T that for a given x yields the amount Tx borne by the cedent. The random variable x is thus divided into two partsand the properties of the reinsurance contract described by T are summarized in the distributions of the two random variables Tx and (1 — T)x = — Tx.The motivation for reinsurance is generally held to be a desire for stability, in other words the cedent wishes to choose a T such that the random fluctuations in Tx are in some sense smaller than those of x. This choice will in our case be performed under the restriction that ETx = m — c.It is clear that we can never talk about an optimal choice of T without defining exactly what criterion we shall use when comparing two transformations, T1 and T2. According to the above, the criterion should refer to the properties of the distributions of T1x and T2x, so that if one distribution is “more concentrated” around some central value, the corresponding transformation is deemed preferable to the other. However, we still have to define what we mean by “more concentrated”.
A Study in Credibility Betterment Through Exclusion of the Largest Claims
Authors: Derron Marcel 
Published: July 2016

It is often found even today in Europe that for certain statistical investigations the conclusion is drawn that the extent of the available statistical data is not sufficient. Going to the root of this pretention, however, we notice that there is a want of clear conception about the extent that is in fact necessary in order that a valid conclusion may with greater probability be arrived at. This, for instance, is the case when obvious tariff reductions are shirked from by entrenching oneself behind the law of large numbers, which by its very nature can in actual practice be never accomplished in its inherent sense.Apart from a proper understanding of the limits within which a set of statistical data may subject to certain assumptions be ascribed full measure of credence, there is further a lack of the necessary tools that would permit, on the basis of ascertainable values alone, far-reaching conclusions to be drawn or a maximum of useful information to be gathered from an investigation of which the scope is evidently not sufficient.Credibility Theory, of which Prof. Mowbray [4] may be regarded as the initiator, was evolved in the U.S.A. about 50 years ago to fill this lacunae. The development of Credibility Theory may be considered as one of the most significant contributions of American actuarial science, and it is frankly astonishing that apart from certain specific realisations in the collective risk theory which are fairly closely related to Credibility Theory, it is only in recent years that this interesting topic has met with the required attention in Europe.
The economic theory of insurance
Authors: Borch Karl 
Published: July 2016

1.1.— Under Subject 4 at this Congress we have discussed the practical application of modern statistical techniques in different branches of insurance. During the last decades, there has been an almost explosive development in theoretical statistics and related branches of mathematics. I think it has been very useful to survey the techniques, which have been developed, and find out if they can be used in insurance.1.2. — There may, however, be some danger in this approach. When new means become available, we should of course have an open mind, and examine these means in order to see if they can serve our ends. We should, however, not get so excited over the power of new techniques, that we distort our ends just for the sake of being able to apply the means.Linear programming, to take an example, is a powerful tool, which has proved extremeiy useful in many, apparently very different fields. There is, however, little point in using this technique in insurance, unless we have problems which consist of determining the maximum of a linear expression, subject to linear restraints. If there are problems in insurance which can be cast in this form, with sufficient approximation, then linear programming is obviously useful. If, however, we lose something essential by reformulating our problems in this way, linear programming may become a dangerous temptation, which we should resist.
Some Models of Inference in the Risk Theory from a Bayesian Viewpoint
Authors: Daboni Luciano 
Published: July 2016

Our purpose is to introduce some models of inference for risk processes. The bayesian viewpoint is adopted and for our treatment the concepts of exchangeability and partial exchangeability (due to B. de Finetti, [6], [7]) are essential.We recall the definitions:The random variables of a sequence (X1, X2 …) are exchangeable if, for every n, the joint distribution of n r.v. of the sequence is always the same, whatever the n r.v. are and however they are permuted.From a structural point of view an exchangeable process X1, X2 … can be intended as a sequence of r.v. equally distributed among which a “stochastic dependence due to uncertainty” exists. More precisely the Xi are independent conditionally on any of a given set (finite or not) of exhaustive and exclusive hypothesis. These hypotheses may concern, for instance, the values of a parameter (number or vector) on which the common distribution, of known functional form, of Xi depends. We shall restrict ourselves to this case. Therefore, we shall assume that, conditionally on each possible value θ of a parameter Θ, the Xi are independent with F(x/θ) as known distribution function. According to the bayesian approach, a probability distribution on Θ must be assigned.
The n-Fold Convolution of a Mixed Density and Mass Function,
Authors: von Lanzenauer Christoph Haehling , Lundberg William N. 
Published: July 2016

AbstractThe distribution of the sum of n mutuality independent random variables with a common distribution f(x) plays an important role in many insurance problems. The paper presents alternative methods of deriving the distribution of the sum of n random variables when f(x) is a mixed density and mass function. The methods are illustrated and compared.
Bayesian Inference in Credibility Theory
Authors: D'Hooge L. , Goovaerts M. J. 
Published: July 2016

AbstractIn 1967, Bühlmann has shown that the credibility formula was the best linearized approximation to the exact Bayesian forecast.His result for the credibility factor can be found back by means of some Bayesian inference techniques. Introducing a uniform prior probability density function for the credibility factor provides us with a method for estimating z, a correction term to the Bühlmann's result is obtained. It is shown how prior boundary conditions can be introduced.
Note on the Background to the Subject: Theory of Risk, Fundamental Mathematics and Applications
Authors: Philipson Carl 
Published: July 2016

By a general theorem the necessary and sufficient condition for a function φ0 (σ) being completely monotonic for σ lying in the right semi-plane, i.e. that the nth derivative with respect to σ has the sign of (— 1)n, is that the function may be represented by the Laplace-Stieltjes integral , where U (v) is a non-decreasing function of v, independent of σ and bounded in every finite interval, σ a real or complex variable represented in the right semi-plane, s a real constant ≤ the real part of σ. By the notation φn (σ) we designate , which for U (v) being independent of σ, as assumed above, is equal to .Definition 1. A compound Poisson process (in the narrow sense) is a process for which the probability distribution of the number of changes in the random function Y (t), constituting the process, occurring while the parameter, which is represented on the positive real axis, is in the interval (o, t) for every value of t, is defined by the following relationthe function φn (σ) being defined by the integral given above and subject to the condition that φ0 (σ) tends to unity, when σ tends to s. The function U (v) in the integrand of φn (σ) is, then, a distribution function which defines the risk distribution, in this case said to be t-independent.
Le test de la majorité confirmée et son utilisation dans l'inference statistique
Authors: Franckx Edouard 
Published: July 2016

J'ai longtemps hésité à donner cette conférence. J'ai craint de déborder largement le cadre des thèmes proposés à Rättvik. Cependant, je pense que la question que je voudrais exposer se rattache plus ou moins à la question que nous avons discutée aujourd'hui et qui consiste à choisir pour un risque déterminé la fonction de distribution adéquate.Ma première réflexion à ce sujet pourra paraître surprenante: je ne suis pas du tout convaincu que nous devons toujours et à tout prix essayer de trouver une représentation analytique du risque étudié. Remarquons que l'on ait ou non une telle possibilité, elle ne change rien au fait que l'on a traité dans le passé et que l'on continue à pratiquer l'assurance des risques divers sans avoir une représentation mathématique plus au moins bien approchée de la fonction de répartition du risque couru).Il y a, par ailleurs, de bonnes raisons de craindre que l'on arrive jamais à une solution unique; en effet ce qui intéresse la Compagnie cédante c'est la partie de la fonction de répartition qui correspond aux petits et moyens sinistres: par contre pour le réassureur c'est la partie relative aux grands sinistres qui importe. Comme dès lors, en pratique, c'est le réassureur qui imposera la distribution correspondant à ses propres risques et qui sera définie à l'échelle internationale. Celle-ci sera tout naturellement différente de celle admise par la Compagnie cédante pour une production plus locale. Il y a là, en fait, des exigences pratiques qui conduisent à des solutions multiples.
Tarification du risque individuel d'accidents d'automobiles par la prime modelee sur le risque
Authors: Delaporte Pierre J. 
Published: July 2016

Le principe de l'assurance contre les accidents d'automobiles est la formation d'une mutualité où les assurés mettent en commun leurs risques. Si les risques des assures ne sont pas tous égaux entre eux, il est normal de demander à chacun des assurés une prime proportionnelle au risque qu'il fait supporter à la mutualité. La tarification a pour objet l'estimation du risque propre à chaque assuré, afín de répartir équitablement la charge totale de la mutualité.On groupe habituellement les véhicules ayant en commun plusieurs caractéristiques du risque telles que même modèle de voiture, même usage, même lieu de garage habituel. Nous désignerons un tel groupement par classe de tarif.On observe les accidents relatifs aux véhicules appartenant à une même classe de tarif. Le quotient du coût de ces accidents au nombre de voitures-année donne la prime moyenne pure empirique. Cette prime moyenne subit alors quelques corrections pour tenir compte de la survenance au hasard des gros sinistres et du fait que la prime à indiquer dans le tarif estime le risque moyen futur et non pas le risque passé Cette prime moyenne sera demandée à toutes les voitures ayant les caractéristiques définies par la classe de tarif; elle suppose que tous les risques de cette classe sont égaux, c'est-à-dire que les seuls paramètres de tarification retenus sont exhaustifs pour caractériser le risque que l'assuré fera supporter à la mutualité.