bluuebunny/crossref_metadata_2025_split huggingface dataset:
L'écrêtement des sinistres “automobile”
Authors: Moreau Par Lionel 
Published: July 2016

SummaryFrench insurance companies usually classify their agents according to their results by branch and to this effect they calculate their respective claim ratios.As regards motor insurance many agents have argued against this practice as they believed it was unfair to be adversely classified when they had the misfortune to incur a large claim.In this article, the merits of various statistical systems for attenuating the effects of large claims on the portfolio are considered in order to come to the most equitable solution possible, i.e., to ascertain the best method and system for attenuating the effects of large claims. The conclusion is that the excess of loss technique is best suited to this effect.To arrive at this conclusion the author of this article relates in detail the various stages of the study, the various systems envisaged and the tests which have allowed to select the most appropriate system. The main results obtained are also given together with their respective drawbacks.At the end of the article the author mentions the still fairly limited bibliography which deals with this question.Dans le but d'améliorer les résultats, les compagnies d'assurance ont l'habitude en France de publier un classement de leurs Agents Généraux basé sur le ratio S/P (sinistres/primes) et de tenir compte de ce classement pour l'attribution de certains avantages commerciaux.Or, en assurance automobile, un malaise profond s'était emparé d'un certain nombre d'entre eux, et ils avaient mis l'accent sur un point qu'ils estimaient injuste:“Nous ne pouvons pas être pénalisés” disaient-ils, “si un très gros sinistre, atteignant 500 ou 1000 fois la prime annuelle, frappe un de nos clients, car il s'agit alors d'un phénomène aléatoire dont nous ne sommes pas responsables”.Telle est l'origine de la politique de l'écrêtement.
Sur la determination d'un contrat optimal de reassurance
Authors: Lemaire Jean 
Published: July 2016

SummaryOhlin [7] showed optimality properties of Stop Loss reinsurance when the ceding insurer uses a continuous loss function to evaluate his risks. We generalize this property to the range of the distribution; we then show that Stop Loss reinsurance is no longer the best form when the company uses a percentile parameter. Finally we prove an optimality theorem concerning chance games which allows us to determine the retention as a function of the size of the portfolio.
Balancing International Insurance Portfolios and Exchange Risks
Authors: Agmon Tamir , Kahane Yehuda 
Published: July 2016

This paper examines the balancing of the investment and liability portfolios of a (re)insurance firm operating in the international market. The model captures two effects which are ignored by traditional analysts.(a) According to the Interest Parity Theorem, the expected changes in the exchange rates should already be reflected in the expected rate of return on foreign investments. Therefore, an insurer operating in a perfect market should be indifferent to the currency denomination of its financial assets.(b) A second effect which has often been ignored is related to the additional risk resulting from the unexpected fluctuations of the exchange rates.The multi-index model suggested in this paper is capable of capturing these effects. The model can be used to examine and analyze alternative policies of the firm operating in international markets. For example, the model can be used to examine whether an insurer should take positions in certain currencies, or rather take a “full-hedge” policy.
Some Personal Reminiscences of the First Twenty Plus Ten Years
Authors: Beard R. E. 
Published: July 2016

Astin is formally twenty years old, or should I say young, and the occasion of the 13th Colloquium being held in the country where it was constituted seems a very suitable opportunity for making a record of the ten years prior to its formal constitution. This is a personal account and sets out facts and impressions which are now becoming coloured by the vagaries of memory; others will have their own impressions of some of the events and I hope will be stimulated to correct any biasses or to supplement the historical record.Inevitably this record will not be complete and I apologise in advance for any significant omissions. Over the years I have accumulated a large mass of correspondence and had hoped to codify this in anticipation of this article but unfortunately a series of complications arising from my move to a part of rural England as a further stage in my retirement programme have delayed sorting through the mass of paper.My interest in non-life insurance was first stimulated when I was involved in the early 1930's in an analysis of the results of Fire and Auto Property business written in the US. This brought me face to face with the differences between the UK and US approach to profit measurement, in particular the real meaning of unearned premiums. The conventional UK method of basing the provision for unexpired risks on 40% of the premiums written during the year led to significant distortion in the emergence of profits (or losses) with an increasing volume of business, a large proportion of which was for periods of three years. Equally the US method of basing a statutory result without any allowance for the equity in the unearned premiums led to further distortions of the true profit, quite apart from the practice, then permitted, of substantial portfolio reinsurance transactions at the close of accounting periods.
Towards an “International Insurance Fund”: A Tool for Mitigation of Extra-Hazard Risks
Authors: Shenhav Yehuda 
Published: July 2016

AbstractIn this paper, the establishment of a new insurance organization, the International Insurance Fund (IIF), is proposed. This organization should undertake to deal with extra-hazard risks which are beyond the capacity of both the commercial insurance industry and national governments. It is proposed that the IIF be designed along the basic lines of the International Monetary Fund (IMF) and its sister organizations.The hypothetical scope of the IIF operations during recent years is illustrated. Certain practical aspects of its actual operations are discussed; some of them call for further examination.
Problems in the Economic Theory of Insurance
Authors: Borch Karl 
Published: July 2016

More than ten years ago I wrote a paper with the title “The Economic Theory of Insurance” [6]. I was not particularly happy about this paper, and I do not think it contributed much to the development of a sastifactory theory. The paper did however make me—and I hope some readers—acutely aware of the difficulties and problems which must be overcome before a proper theory can be constructed. These problems are still unsolved, so I have on the present occassion chosen a more modest title for a paper on substantially the same subject.Insurance is an economic activity of some importance, and there is an obvious need for a theory to explain and analyse the activity in the insurance sector of the economy. During the last decade many economists seem to have felt the need, and to have taken it as a challenge. The results have been a fair amount of research, and a number of publications, which I shall not try to review here. It may however be useful to refer to three very recent survey articles by Farny [10], Ferry [11] and Rosa [14], which give extensive bibliographies. The three articles seem to indicate that the economics of insurance is becoming a fashionable subject of research.
Testing Goodness-of-Fit of an Estimated Run-Off Triangle
Authors: Taylor G. C. 
Published: July 2016

By the term actual run-off triangle we shall mean the two-way tabulation—according to year of origin and year of payment—of claims paid to date, which has the following form:where Cij is the amount paid during development year j in respect of claims whose year of origin is i.The information relating to the area below and/or to the right of this triangle is unknown since it represents the future development of various cohorts of claims.Now in seeking to use this triangle as a basis for projection of claims in future development years for each of the years of origin 0, 1, 2, etc., we must recognise that the entries Cij in the above triangle, being random variables, contain random deviations from their expected values uij. It is the corresponding triangle of these expected values in which we are interested, and which shall be called the expected run-off triangle.
Parameter Estimation in Credibility Theory
Authors: De Vylder Fl. 
Published: July 2016

AbstractThe problem of distribution-free parameter estimation in recent credibility theory is discussed in the papers [1], [3] and [4] of the bibliography. Here, we consider a multiclass model with regression assumption. In that case, already treated by Ch. Hachemeister, [3], this author obtains an unsymmetrical matrix as an estimator of a covariance matrix. Of course, for practical use, this matrix is symmetrized in the obvious way. We show that this procedure can be avoided and that a lot of symmetrical unbiased estimators can be obtained at once.By particularisations to the 1-rank model, we find the estimators given by Bühlmann and Straub, [1], [4].In the multirank case, a generalization of the minimumvariance principle (minimization of the trace of the covariance matrix) leads to an optimal estimator of the mean regression vector. A noteworthy conclusion of our discussion is that there is no difference at all between the various credibility formulae (the inhomogenous formula, the homogeneous formula, the meanfree formula) if the mean regression vector is estimated optimally.Finally we show that it must not be hoped to find, in a large set of unbiased estimators of the covariance matrix, one estimator furnishing, always, a semidefinite positive estimate.
A Non Symmetrical Value for Games without Transferable Utilities; Application to Reinsurance
Authors: Lemaire Jean 
Published: July 2016

We define axiomatically a concept of value for games without transferable utilities, without introducing the usual symmetry axiom. The model—a generalization of a previous paper [6] extending Nash's bargaining problem—attempts to take into account the affinities between the players, defined by an a priori set of “distances”. The general solution of all three- and four-person games is described, and various examples are discussed, like the classical “Me and my Aunt” and a reinsurance model.Nous définissons de manière axiomatique un concept de valeur pour les jeux à utilités non-transférables, sans introduire l'axiome classique de symétrie. Le modèle — une généralisation d'un concept de valeur [6] étendant à plusieurs joueurs le problème de marchandage de Nash — tient compte des affinités entre les joueurs, données sous forme d'une matrice de “distances” a priori. Nous donnons la solution générale de tous les jeux à trois et quatre joueurs, et discutons plusieurs exemples classiques, dont le célèbre “Ma tante et moi” et le modèle de réassurance de Borch.
An Economic Premium Principle
Authors: Hans Bühlmann  
Published: July 2016

(a) The notion of premium calculation principle has become fairly generally accepted in the risk theory literature. For completeness we repeat its definition:A premium calculation principle is a functional assigning to a random variable X (or its distribution function Fx(x)) a real number P. In symbolsThe interpretation is rather obvious. The random variable X stands for the possible claims of a risk whereas P is the premium charged for assuming this risk.This is of course formalizing the way actuaries think about premiums. In actuarial terms, the premium is a property of the risk (and nothing else), e.g.(b) Of course, in economics premiums are not only depending on the risk but also on market conditions. Let us assume for a moment that we can describe the risk by a random variable X (as under a)), describe the market conditions by a random variable Z.Then we want to show how an economic premium principlecan be constructed. During the development of the paper we will also give a clear meaning to the random variable Z:In the market we are considering agents i = 1, 2, …, n. They constitute buyers of insurance, insurance companies, reinsurance companies.Each agent i is characterized by hisutility function ui(x) [as usual: ]initial wealth wi.In this section, the risk aspect is modelled by a finite (for simplicity) probability space with states s = 1, 2, …, S and probabilities πs of state s happening.
Survival Probabilities Based on Pareto Claim Distributions: Comment
Authors: Goovaerts Marc J. , de Pril Nelson 
Published: July 2016

In a recent paper Seal (1980) calculated numerically survival probabilities based on Pareto claim distributions.The Pareto density may be written asGeneralizing, the Pareto distribution may be regarded as a special case of the so-called beta-prime distribution (Keeping, 1962, p. 83) with density functionwhere B(p, q) = is the beta function.In his paper Seal (1980, Appendix 1) arrived at a contradiction concerning this beta-prime distribution. He found on one side that all derivatives of the characteristic function exist at the origin and on the other side that only the moments of order n < q exist. In this note we will show that this contradiction is due to the use of an incorrect expression for the characteristic function of the beta-prime distribution, which was taken over from Johnson and Kotz (1970, Ch. 26) and Oberhettinger (1973, Table A).
Speed of Finalization of Claims and Claims Runoff Analysis
Authors: Taylor G. C. 
Published: July 2016

SummaryTo some extent, this paper provides theoretical back-up for Taylor's (1980b) see-saw method of analysis of outstanding claims.Section 3 deals with the payments per claim finalized (PPCF) method. This assumes PPCF to be a function of development year only.Section 4 carries out a theoretical investigation of the validity of this assumption. It is found that the assumption is not justified in general; that PPCF can (and usually will) be sensitive to changes in speed of finalization of claims; and that this sensitivity will depend on the convexity properties of PPCF as a function of development year. The analysis is made on the basis of the so-called hypothesis of invariant order.Section 5 develops the see-saw method from this theoretical basis, although Section 7 is at pains to point to situations in which that method remains applicable despite violation of the hypothesis of invariant order.Section 6 provides a numerical example.
The Esscher Premium Principle: A Criticism. Comment.
Authors: Gerber Hans U. 
Published: July 2016

Zehnwirth (1981) contains some flaws. Ifis the Esscher premium for a risk X, the loading is H(X) — E(X) and not h as Zehnwirth states. The first and third formulas on page 78 are wrong, since o(h) is a quantity such thatA correct statement would have been thator simply that H(X) is a continuous function of the parameter h. However, this continuity is not uniform in all risks, which is illustrated by (3). No matter how small h is, there is always an X such that the difference between H(X) and E(X) is substantial. In view of this what is the meaning of a statement like “… the Esscher premium is a small perturbation of the linearized credibility premium”?
The Swedish Systems of Bonus
Authors: Philipson Carl 
Published: July 2016

According to the provisions of the Swedish tables of rates the premium payable on a certain policy both for Third Party Liability and for Car Damage Insurance (without clause for particular self retention) is equal to the initial premium reduced with regard to points earned as related to years with no indemnities. One such point is earned for each year during which no indemnity has been paid on the policy; upon an indemnity one or two points are lost. The detailed rules for the reduction have been altered from time to time, the existing rules have been valid from the year 1952, these rules will here be called system II, while system I denotes the rules valid during the years immediately previous to 1952. The systems are described in the following table.The probabilities for the occurrence of a claim and for the occurrence of a lapse for a policy can be considered functions of two variables, the points obtained in the bonus scale, b, and the “duration” i.e. the time elapsed since the policyholder signed his first policy, τ. For simplicity two kinds of models have been constructed, one assuming the probabilities to depend only on τ, the other assuming the probabilities to depend only on b.
Remarks on Statistical Distribution of Intensity of Chance Damages
Authors: Banasinski Antoni , Wanatowski Antoni 
Published: July 2016

Actuaries of Polish National Insurance are in the happy position that they have at their disposal a wealth of complete statistics which permits study of the level of chance damage (the loss-rate) and its elements such as frequency of occurrence, spread, intensity, etc. This welcomed situation stems from the fact that in Poland there is general insurance in certain sectors of the national economy. For instance, in the case of cooperative and individual (private) farms the entire property (buildings, products, livestock, real estate and machines, household furniture, etc.) is insured according to uniform principles against all hazards—fire, winds, floods, hail, death of animals and others.This, among other things, makes possible the statistical determination of the intensity of chance damages (i.e. the extent of damage to a given object during one accident) in various elements of farm property.Studies of this type have been of great practical importance in the activities of Polish National Insurance, first and foremost in the reconstruction of the insurance rates in connection with a change in the system to the “first risk” system (employed almost exclusively at present in farm insurance). Moreover, it is interesting that these studies have also served as auxiliary material in the elaboration of the optimum programme for the utilization of the funds allocated for preventing chance damages.Studies on the distribution of the intensity of chance damages on insured objects have led to interesting results which have confirmed once again that this distribution is dependent on the structure of the objects insured and on the risks (hazards) covered by insurance protection; any hypotheses concerning these distributions must be verified in each case by trial statistical studies.
A propos de la distribution des cas de maladie entre les assurés et par rapport à la durée
Authors: Coppini Mario Alberto 
Published: July 2016

Il est un fait bien connu que la technique des assurances, qu'elles soient privées ou sociales, qui versent une indemnité en cas de maladie, se base premièrement sur la connaissance des fréquences et des durées moyennes de maladie, ou bien des coefficients de morbidité. Pour résoudre des problèmes particuliers, des instruments plus raffinés sont toutefois nécessaires, savoir:a) la distribution des assurés d'après le nombre de cas dont ils ont été frappés au cours d'une année;b) la distribution des cas d'après la durée en jours;c) la distribution des assurés d'après les jours de maladie dont ils ont été frappés au cours d'une annèe.Nous avons eu la possibilité d'elaborer les fiches de 44.829 travailleurs salariés (36.134 hommes et 8.695 femmes âgés de 15 à 65 ans) résidant à Rome et assurés obligatoirement auprès de l'Institut National d'assurance-maladie (Istituto Nazionale per l'assicurazione contro le malattie — INAM), et de relever les cas de maladie qui les ont frappés au cours de l'année 1960, en même temps que les durées correspondantes.).Puisqu'il s'agit, comme on le verra, de données très détaillées, il nous a paru utile d'étudier les caractéristiques principales des trois distributions en question et les relations existant entre elles: l'exposé de certains résultats obtenus dans ce sens constitue l' objet de la présente note.
A Numerical Method of Finding a Suitable Bonus Scale
Authors: Pesonen Erkki 
Published: July 2016

The bonus system used by Finnish insurers is as follows: Policies are divided into 4 bonus classes, C1, C2, C3, C4, each of them being initially placed in class C1. After one claimless year, a policy placed in class Ch is transferred to class Ch+1 (h ≤ 3) from the beginning of the following year. After a claim year, each policy is entered back to class C1. (Whether the number of claims is one or more does not play any role in this transition system.) From the initial premium, i.e. the premium in class C1, a reduction of pi, per cent is granted in class Ci. In numbers these percentages are as follows:
In present investigations there is a trend to replace this scale by another in which mere contingency would not cause too great a change in the premium and in which the „test period” would be longer.Let us suppose that we want to find a suitable percentage scale P = (P1, P2, …, Pm) for a bonus system (Cl, C2, …, Cm) with a given transition mechanism according to which for each bonus class Ch two bonus classes Ci and Cj are given to which the policy is transferred after one year from Ch according as there have been claims or not.
“Estimating incurred claims”
Authors: Benedikt V. , Feay Herbert L. 
Published: July 2016

Mr. Benedikt uses “chain relatives” based on the incurred claim totals included in Part 5 of Schedule “P” of the annual statement required for fire and casualty companies in the United States. Each total is for the losses as developed to end of calendar year (j) for claims incurred because of accidents in calendar year (i). Each total is the sum of the actual payments made before the end of year (j) plus the reserve for estimated payments to be made after the end of year (j) for claims incurred in year (i). The “chain relatives” are ratios. The “chain relative” ai,j is the ratio of developed losses to end of (j + 1) to the developed losses at the end of year (j).Each total of Part 5 of Schedule “P” equals the sum of the total payments to date plus the total reserves for future payments for the corresponding classification of claims. Separate totals for these amounts are given in Part 1 of Schedule “P”. The totals of Part 5 are not secured directly from Part 1 because Part 1 gives totals by policy year of issue only and Part 5 separates the totals by policy of issue by calendar year in which claims are incurred. The two parts are prepared from the same basic claim information and agree in total.The accumulated total paid losses for most casualty lines increase with passage of time. This accumulated total for paid losses can be reduced only if there are recoveries for losses previously paid, such as can occur for auto collision. For auto collision, the insurance company for this insurance can pay the insured for the damage to his car and then later recover from the insurance company that provided the liability insurance for another car involved in the same accident. Such substantial recoveries normally do not occur for auto liability insurance for bodily injury and property damage.