bluuebunny/crossref_metadata_2025 huggingface dataset:
A novel social network mining approach for customer segmentation and viral marketing
Authors: Helal Nivin A. , Ismail Rasha M. , Badr Nagwa L. , Mostafa Mostafa G. M.
Published: July 2016

Emergence of social networks facilitates individuals to communicate, share opinions and form communities. Organizations benefit from social networks in monitoring customers’ behavior. Social networks mining and analysis aims to segment customers and determine the most influential actors for viral marketing. In this article, we propose a novel social network mining approach for influential analysis and community detection. The community detection task benefits from the most influential users in the network. The proposed approach identifies the most influential users by using a direct mining leaders discovery algorithm and uses these leaders as core points to expand communities around them. This is based on the observation that communities tend to be formed around users of great influence. Extensive experiments have been completed on a real dataset and results show that our approach can contribute in identifying communities of high quality. WIREs Data Mining Knowl Discov 2016, 6:177–189. doi: 10.1002/widm.1183

This article is categorized under:

Fundamental Concepts of Data and Knowledge > Motivation and Emergence of Data Mining

Technologies > Structure Discovery and Clustering
A general comparison between tokamak and stellarator plasmas
Authors: Xu Yuhong
Published: July 2016

This paper generally compares the essential features between tokamaks and stellarators, based on previous review work individually made by authors on several specific topics, such as theories, bulk plasma transport and edge divertor physics, along with some recent results. It aims at summarizing the main results and conclusions with regard to the advantages and disadvantages in these two types of magnetic fusion devices. The comparison includes basic magnetic configurations, magnetohydrodynamic (MHD) instabilities, operational limits and disruptions, neoclassical and turbulent transport, confinement scaling and isotopic effects, plasma rotation, and edge and divertor physics. Finally, a concept of quasi-symmetric stellarators is briefly referred along with a comparison of future application for fusion reactors.
Buckling of Cylindrical Shells with Arbitrary Circumferential Thickness Variations Under External Pressure
Authors: Feng W.-Z. , Chen Z.-P. , Jiao P. , Zhou F. , Fan H.-G.
Published: July 2016

This paper presents an analytical study on the buckling of cylindrical shells with arbitrary circumferential thickness variations under external pressure. Firstly, based on the thin shell theory and separation of variables, corresponding ordinary differential equations of laterally pressured cylinders are obtained. Secondly, the general asymptotic formula of buckling load, which is in terms of thickness variation parameter up to arbitrary order, is derived by combining the perturbation method and Fourier series expansion. Thirdly, the effects of uniform and circumferential modal thickness variations on the buckling of cylindrical shells under external pressure are investigated, respectively, and the results agree well with those available in literature. Particularly, the buckling load reduction of cylinders with circumferential modal thickness variation obtained by the proposed method coincides with the numerical results presented by Gusic et al. This analytical method is applicable for evaluating the stability of laterally pressured cylindrical shells with arbitrary circumferential thickness variations, once the thickness variation is known.
Democratic Accountability and the Politics of Mass Administrative Reorganization
Authors: Bertelli Anthony M. , Sinclair J. Andrew
Published: July 2016

Governments face different incentives when they reorganize many administrative agencies at one time rather than making infrequent, case-by-case changes. This article develops a theory of mass administrative reorganizations, which posits that the politics of reorganization is focused on government accountability. Viewing mass reorganization as a structured decision, it argues that choices about independence, agency organization and functional disposition have different impacts on the political costs of administrative policy making. Analyzing novel data from a recent British reorganization with sequential logistic statistical models provides substantial support for these claims. The study challenges the focus on organizational survival in the existing literature. By eschewing more fundamental political questions of democratic accountability, the prevailing approach masks essential politics, and in the context of this study, all influence of conflict due to party and agency policy positions.
A Jewish Riot against Muslims: The Polemics of History in Late Colonial Algeria
Authors: Schreier Joshua
Published: July 2016

On Rosh Hashanah, 1961, six months before the conclusion of the Evian accords promised independence for Algeria, riots broke out in the city of Oran. Surprisingly to many, the aggressors were overwhelmingly Jews, while those injured or killed were largely Muslims. The events—widely covered in the media but since forgotten—were a product of Oran's particular social chemistry, but were also shaped by far wider set of debates about a chasm that was growing between Jews and Arabs in France, Algeria, and the wider Arab world. This article focuses on responses to these riots, especially how they drew on polemical renderings of a shared Muslim-Jewish history. I make two interrelated arguments based on printed matter of the period, French government archives, and memoirs. First, Algerian Jewish observers and pro-FLN nationalist writers, groups that only rarely agreed on the question of Algerian independence, both recalled that the two groups' shared a largely harmonious history. They vehemently disagreed, however, on what this shared, harmonious history meant in terms of political obligations. The article's second argument is that the Israel-Palestine conflict helped sour relations between Jews and Muslims in Algeria, as well as historical renderings of these relations, during the Algerian War of Independence. Specifically, the question of Palestine frequently appeared as a reference when interpreting the riots. Together, the two arguments demonstrate how international issues helped occlude the particular, local stories and belongingness of Algerians, while they defined the future, religio-ethnic contours of the Algerian nation.
Legitimising the care market: the social recognition of migrant care workers in Italy
Authors: CORDINI MARTA , RANCI COSTANZO
Published: July 2016

The sizeable presence of migrant care workers in the private care market in many European countries is confirmed by several studies that have explained the phenomenon through functional arguments, stressing the economic convenience of transnational markets and the crucial role played by public regulation. This paper focuses instead on the public and institutional discourses that have contributed to legitimising this private care market, characterised by the worsening of employment conditions and the decrease in care quality. The main argument of this paper is that the social recognition of these workers provides the public with the new concepts and rationales that determine the actual shape of the private care market.

Migrant care workers are usually, compared to other migrant workers, more welcome in the host society and less targeted by xenophobic attitudes, especially where their labour helps to meet a lack of public provision as is happening in Southern European countries. Nevertheless, their rights are not fully granted either as citizens or as workers: basic requirements in this migrant care market include for instance reduced wages, great flexibility, and informal contracts.

Our hypothesis is tested through the reconstruction of the public regulation and a content analysis of the public discourse that has accompanied this regulation for ten years (2002–2012) in Italy. The two main national newspapers have been taken into account. This analysis provides evidence on how market dynamics have been shaped by a deliberate political construction, which has relieved governments of the task of finding a public solution to care needs and has relegated migrant care workers to a subordinate social position, which is functional in making the care market work.
Actuarial Activity in General Insurance in the Northern Countries of Europe
Authors: Wilhelmsen L.
Published: July 2016

Although actuaries have been connected with life insurance business for more than 100 years, it is only more recently that actuarial activities in the non-life branches have taken place.

The problem of calculating level premiums for the steadily increasing risk in life insurance immediately calls for mathematical ability. The need for mathematically trained specialists is not so easily seen when the problem is to calculate premium rates for fire and casualty insurances. The premium rates in this field have to a great extent been fixed by persons with none or very little knowledge in mathematics and mathematical statistics. When the market conditions allow for considerable margins this arrangement works out very well. The statistical investigation needed later on for controlling the premium rates is not very complicated, and the premium rates can if necessary be changed on short notice. A mistake made in the premium stipulation, will generally not have a lasting effect. In life insurance on the other hand, the contracts often stretch over many years and a mistake in the premium stipulation cannot easily be corrected. These circumstances explain the reason why actuaries have been more often engaged in life insurance than in the fire and casualty branches.

But a closer study shows that from a mathematical point of view, the proper fixing of premium rates is often more complicated in the fire and casualty branches than in life. In the fire and casualty field a steady changing of market conditions seems to take place. The competition grows keener and keener, and the margins are cut down. Sooner or later we reach a point where it is of vital importance to know as exactly as possible where we stand. This means that we have to study the risk premium, the security loading and the expense loading separately, and to estimate these quantities with the highest efficiency.
ASTIN Memoirs
Authors: Johansen Paul
Published: July 2016

Nous avons pensé que les assurances contre l'incendie pouvaient aussi s'étayer du calcul. (T. J. Barrois, 1835)

To a mathematician 25 is a very uninteresting number: Just the square of a small prime. For a historian it means an epoch. If 25 years bring us back to one of the cataclysms of recent history, then it is worth looking back at them. (S. Vajda, 1964)
An Application of Game Theory: Cost Allocation
Authors: Lemaire Jean
Published: July 2016

The allocation of operating costs among the lines of an insurance company is one'of the toughest problems of accounting; it is first shown that most of the methods used by the accountants fail to satisfy some natural requirements. Next it is proved that a cost allocation problem is identical to the determination of the value of a cooperative game with transferable utilities, and 4 new accounting methods that originate from game theory are proposed. One of those methods, the proportional nucleus, is recommended, due to its properties. Several practical examples are discussed throughout the paper.
Claims frequency and risk premium rate as a function of the size of the risk
Authors: Benktander Gunnar
Published: July 2016

The rapid economic growth in the last decade and the fierce competition have forced industry to raise its output, to develop new manufacturing methods and, where possible, to lower the fixed costs per unit of output. Consequently bigger factories and warehouses have been and are being built. Furthermore increasing labour costs have speeded up rationalisation and the introduction of efficient machinery.

Often, in the course of this development, too little attention has been paid to safety. This is reflected in the increasing number of Fire and Consequential Loss claims which have become so costly that the premium income has proved inadequate. Insurers have therefore adjusted their tariffs and increased their rates.

Of course, this is no solution to the problem. Insurers have to insist on adequate fire prevention and fire protection measures. Progress in the right direction can certainly be expedited by realistic tariffs which take account of all the positive features (sprinklers, inspection reports, etc.) and the negative features of a given risk (in commerce or industry).

Rating experts say that the tariffs of industrialized countries do not always point to the actual risk and claims fluctuations; one very important factor here, the size of the risk or of the building (i.e. its insured value, volume, surface area), brings me to the main theme of my today's talk.
Mathematical Models in Insurance
Authors: Borch Karl
Published: July 2016

This paper contains little which can be considered as new. It gives a survey of results which have been presented over the last 10-15 years. At one time these results seemed very promising, but in retrospect it is doubtful if they have fulfilled the expectations they raised. In this situation it may be useful to retrace one's steps and see if problems can be reformulated or if new approaches can be found.

Mathematical models have been used in insurance for a long time. One of the first was the Gompertz mortality law; a more recent model, which has been intensively studied is the Compound Poisson Distribution in Lundberg's risk theory.

When a model is introduced, one usually proceeds by stages. The first step is to see if the model appears acceptable on a priori reasons. If it does, the second step is to examine the implications of the model, to see if any of these are in obvious contradiction with observations. If the result of this examination is satisfactory, the third step is usually a statistical analysis to find out how well the model approximates the situation in real life, which one wants to analyse. If the model passes this second examination, the next and final step may be to estimate the parameters of the model, and use it in practice, i.e. to make decisions in the real world.

The advantage of working with a model is that it gives an overall purpose to the collection and analysis of data. A good model should tell us which data we need, and why.
An Investigation of the Use of Weighted Averages in the Estimation of the Mean of a Long-Tailed Claim Size Distribution
Authors: Taylor G. C.
Published: July 2016

The paper discusses the problem of estimating the mean of a long-tailed claim size distribution when the investigator's knowledge of the distribution is only vague.

One method of dealing with this problem, the method developed by Johnson and Hey, is examined and found to produce strongly biased estimators.

The situation in which a sufficient statistic (but nothing else) for the claim size distribution is known is examined, and an approximately unbiased estimator developed. This estimator is substantially more efficient than the arithmetic mean in some cases. It appears to be quite successful when the sufficient statistic is real-valued. It is of limited use when the sufficient statistic is vector-valued.
An Illustration of the Duality Technique in Semi-Continuous Linear Programming
Authors: De Vylder F.
Published: July 2016

We gıve a complete parametrıc solutıon of the followıng problem: Fınd a claım sıze dıstrıbutıon F on the fınıte ınterval [ο, ω], maxımizıng the stop-loss premıum correspondıng to a gıven excess e, under the constraınts that the fırst moment of F be at most equal to μ and the second at most equal to ν The method used ıs the dualıty technıque ın semı-contınuous lınear programmıng descrıbed in De Vylder (1978) Thıs technıque ıs summarızed, wıthout proofs, ın the fırst part of the paper.
Recursions for Compound Distributions
Authors: Panjer H. H. , Willmot G. E.
Published: July 2016

Various methods for developing recursive formulae for compound distributions have been reported recently by Panjer (1980, including discussion), Panjer (1981), Sundt and Jewell (1981) and Gerber (1982) for a class of claim frequency distributions and arbitrary claim amount distributions. The recursions are particularly useful for computational purposes since the number of calculations required to obtain the distribution function of total claims and related values such as net stop-loss premiums may be greatly reduced when compared with the usual method based on convolutions.

In this paper a broader class of claims frequency distributions is considered and methods for developing recursions for the corresponding compound distributions are examined. The methods make use of the Laplace transform of the density of the compound distribution.

Consider the class of claim frequency distributions which has the property that successive probabilities may be written as the ratio of two polynomials. For convenience we write the polynomials in terms of descending factorial powers. For obvious reasons, only distributions on the non-negative integers are considered.
Distribution du coût d'un sinistre dans l'assurance sociale contre les accidents
Authors: Latscha R.
Published: July 2016

On n'a guère entendu dire jusqu'ici que la distribution empirique du coût d'un sinistre dans l'assurance sociale en cas d'accidents ait fait l'objet d'études spéciales. Comme la Caisse nationale suisse d'assurance en cas d'accidents est en train de faire de tels examens en vue de résoudre certains problèmes de tarification que pose l'application de la théorie du risque, nous avons pensé qu'il serait intéressant de présenter une courte communication à ce sujet). Le présent rapport a pour objet l'étude des fonctions empiriques de la distribution du coût d'un accident professionnel dans cinq branches industrielles et artisanales en Suisse). Nous voudrions faire précéder notre exposé de quelques considérations sur l'organisation et les tâches de l'assurance sociale contre les accidents en Suisse ainsi que de l'énumération des désignations et abréviations employées dans ce rapport.

La Caisse nationale suisse d'assurance en cas d'accidents à Lucerne, en fonction depuis 1918, est un établissement de droit public autonome. Elle assure obligatoirement contre les conséquences économiques des accidents professionnels et non professionnels les ouvriers et employés des entreprises soumises à l'assurance conformément à la loi sur l'assurance en cas de maladie et d'accidents de 1911. Sont considérés comme accidents professionnels les accidents qui se produisent pendant le travail dans l'entreprise ainsi que les maladies professionnelles. Tous les autres accidents, notamment ceux qui se produisent sur le chemin pour se rendre au travail et en revenir, sont des accidents non professionnels. L'assurance des accidents professionnels et celle des accidents non professionnels forment deux branches d'assurance distinctes. Dans les deux branches, les prestations d'assurance sont les mêmes. Elles consistent dans le paiement des frais de traitement, d'une indemnité de chômage ainsi que dans l'octroi de rentes d'invalidité et de survivants.
Reinsurance of Third Party Motor Insurance and Motor Insurance in Finland
Authors: Pentikäinen Teivo
Published: July 2016

The need and extent of reinsurance of third party motor insurance depends fundamentally on the risk limits prescribed in the legislation of the country in question (and on the other hand the legal limits of the compulsory insurance may have been fixed with regard to the reasonable possibilities of the insurers getting reinsurance). There are two kinds of risk limits which are applied in different countries: total limits and individual limits. The former defines the maximum joint indemnity for an accident, paid to all claiments together, and the latter defines the maximum indemnity paid to each claiment separately. From the social point of view limits of this sort are not expedient, especially in regard to physical injuries. Owing to this total limit the indemnity for a single claiment can depend on the number of other claiments, which is quite inadequate from the point of view of the actual need to get insurance cover for injuries. The individual lump sum limit allows full compensation for slight injuries but can cut down the compensation for serious ones, which is an irrational method of settling an indemnity system. Owing to these risk limits motor car drivers may also be held responsible for the extra claims personally on the basis of civil (or criminal) law, which compels them to take an extra third party liability insurance (which often also has risk limits).
Reassurance du Cumul D'Accidents
Authors: Sousselier Jean
Published: July 2016

Une Compagnie d'assurances délivre par l'intérmediaire d'Agences de Voyage des contrats d'assurances individuelles garantissant les personnes prenant place dans des autocars contre les décès par accident. Le capital garanti est uniforme. Il sera pris égal à I par simplification.

Cette Compagnie prend à sa charge le paiement de i décès au maximum dans chaque accident et demande à un Réassureur de payer, aux termes d'un traité en excédent de sinistre, les autres décès; autrement dit, si un accident cause d décès, la Compagnie paie I, le Réassureur en excess paie d — I.

Il s'agit de calculer la prime de ce traité en excédent de sinistre?

La solution dépend de trois paramètres:

n nombre de passagers par autocar, égal au maximum au nombre de places; on supposera, pour fixer les idées, n = 502).

d nombre de décès survenus dans un même accident. C'est une variable stochastique comprise entre 0 et n.

Il n'y a pas lieu de faire intervenir la fréquence d'accidents (entraînant des morts) q, car celle-ci est un des éléments constitutifs du tarif appliqué par la Cédante et la prime de réassurance est exprimée comme une fraction de la prime originale. Si celle-ci est incorrecte, trop basse ou trop élevée, l'Assureur réalise une perte ou un bénéfice et il est normal que le Réassureur suive en cela la fortune de sa Cédante. La seule question est celle d'un partage équitable de la prime perçue, bonne ou mauvaise, entre la Cédante et le Réassureur.
The insurer's ruin
Authors: de Jongh B. H.
Published: July 2016

This paper was written in connection with the preparation of Marché Commun regulations in the insurance sector and has been submitted to the Commission Technique pour l'étude d'un indice de solvabilité relatif aux entreprises d'assurances contre les dommages. It aims at explaining the scope of the problem to non-mathematicians and for that reason emphasizes its logical in contradistinction to its computational aspects.

The probability of the insurer's ruin has two aspects. The occurrence of the event ruin may be considered with respect to a fixed period but also with respect to a period of undetermined length. In both cases the period starts at a moment at which the insurer's capital (patrimoine) is known and it is intuitively clear that in both cases the probability of ruin will be the higher as the insurer's capital is smaller and the risk to which he is exposed heavier.

For some purposes more precise conclusions are required. This requirement gives rise to problems which will be considered here with respect to the probability of the occurrence of ruin in a period of undetermined length. It will be taken for granted that besides the artificial events occurring in games of chance there are other classes of uncertain events to which numerical probabilities can be assigned and that, as far as claims are concerned, the insurer's losses belong to one of the said classes. On this understanding it makes sense to consider a numerical probability of ruin depending on a fixed initial capital, random losses to which numerical probabilities are assigned, and other profits and losses.
Experience Rating When the Company Aims to Increase the Volume of its Business
Authors: Bohman Harald
Published: July 2016

An insurance company aims to increase the volume of its business.

The volume is measured by the premium income during one year.

The company makes use of N tariff groups.

pn = premium charged by the company per unit of insurance in tariff group n.

qn = premium per unit of insurance in tariff group n corresponding to the statistical experience in the said group.

Ln = The size of the market in tariff group n. If all insurances in the group pay the same premium and if the company is able to cover the whole of its potential market then Ln is equal to the number of policies. If the premium per policy is equal to pn times the sum insured and if the company is able to cover the whole of its potential market then Ln is equal to the total sum insured.

Fn(p) = the proportion of Ln that actually buys insurance in tariff group n if the company charges the premium p per unit of insurance.
Magnitude control of technical reserves in Finland
Authors: Pesonen Erkki
Published: July 2016

This paper deals with some requirements put forward by the Finnish Supervisory Service on technical reserves mainly for solvency reasons. Consequently only one but nevertheless an important aspect of solvency problem is touched upon. The solvency question in its entirety is discussed in a paper of Dr. Pentikainen at this same colloquium.

According to the instructions of the Supervisory Service, given by virtue of the Insurance Companies Act, insurance companies are obliged to calculate a so-called equalisation reserve in a specific way. Simplifying slightly, this equalisation reserve is that part of the technical reserves which exceeds the premium reserve and the claims reserve calculated according to classical actuarial principles; that is to say, the present value of the expectation value of the net insurance liabilities. The Insurance Companies Act calls for this reserve because conventional technical reserves do not take into account the random feature of claims amount.
Some Analyses of Car Insurance Claim-Rates
Authors: Munden J. M.
Published: July 2016

We have printed the foregoing paper by Mr. Munden as submitted because we think that the detailed analysis will be of interest to all who have interests in the field of motor insurance rating. Of necessity, the data does not lend itself to analysis with respect to some of the known variables and we are conscious that some of the conclusions are controversial; some factors have also emerged from the discussions within ASTIN on motor insurance and it is therefore hoped that the following comments will be of value in relation to the paper.

It is of the utmost importance that a clear distinction is drawn between the concept of accident proneness and the heterogeneity shown from observations of claim frequencies under insurance policies. As the discussion at La Baule brought out, the first conclusion to be derived when a compound Poisson distribution emerged is that there is a degree of heterogeneity in the data. This might be due to differences in accident probabilities of the underlying risks, but it could be due, for example, to different exposures of similar risks. Lanteli's paper to the Rättvik colloquium showed a substantial variation of claims experience with annual mileage and thus without an analysis controlled with respect to mileage the conclusion that a proneness factor is solely involved must be suspect.
On the Use of Linear Discriminant Functions in the Realm of Industrial Accident Insurance
Authors: van Klinken J.
Published: July 2016

Discriminant analysis is an application of multivariate analysis, which may have its use in determining accident risk levels and premiums of industrial enterprises. This paper only aims to give some suggestions. The following questions will be considered.

1. Determining a discriminant function which makes it possible to discriminate between the risk levels of the industrial branches in an efficient way. The industrial branches comprise enterprises with comparable risk levels, hence they are to be considered as homogeneous groups. The function will at the same time serve as a means to classify seperate enterprises into one of these groups.

2. Fixing risk functions which enable us to rank the enterprises of an industrial branch to increasing risk on the ground of observations of a number of variates which characterize the risk situation.

3. Using these risk functions to calculate premiums. The classification-question mentioned under I was the reason to consider the technique of the discriminant analysis. By virtue of the Dutch Industrial Accidents Act every five years a tariffdecree is being published. This decree contains the premiums per wage-unit for the industrial branches. However, there are enterprises e.g. large compound enterprises which do not fall under these regulations. These enterprises ought to be classified according to their own experience. That means we need the knowledge of the risk levels of these particular enterprises in relation to the fixed risk levels of the industrial branches. As mentioned, this is a problem inherent to the typical Dutch situation. It seems, however, probable that such problems and the techniques we intend to sketch have a wider and more general meaning for the accident insurance.
A Combination of Surplus and Excess Reinsurance of a Fire Portfolio
Authors: Benktander Gunnar , Ohlin Jan
Published: July 2016

Reinsurance forms can roughly be classified into proportional and non-proportional. The authors of this paper had planned to investigate the “efficiency” of two different reinsurance forms, one from each of these categories. Efficiency is here understood as reduction in the variance of the annual results of the risk business achieved per unit of ceded reinsurance risk premium. This investigation may be carried out in full later.

This note will only deal with the interplay between surplus and excess of loss reinsurance; more specifically the effect of changes in the volume of surplus cessions on the excess of loss risk premium.

The study came out of a practical Fire Reinsurance rating problem and will be carried through under very simplified assumptions. Thus we will ignore the conflagration hazard and the possibility of a wrongly taxed PML. This means that if amounts above a PML of M are ceded on a surplus basis the highest loss per event will be M, and an excess cover above a priority m will never pay more than M-m per event.

The following notations will be used

R(M) ceded risk premium volume on surplus basis, the PML retention being M.

πM(m) excess of loss risk premium if priority is m and surplus cessions are made above a PML of M.
Application of Reliability Theory to Insurance
Authors: Straub E.
Published: July 2016

1. There is a general rule applicable to all insurance and reinsurance fields according to which the level of the so-called technical minimum premium should be fixed such that a certain stability criterion is satisfied for the portfolio under consideration. The two bestknown such criteria are

(i) the probability that there is a technical loss in any of the future years should be less than a given percentage

(ii) the probability that the company gets “ruined” i.e. initial reserves plus accumulated premiums minus accumulated claims becomes negative at any time of a given period in the future should be less than a tolerated percentage.

Confining ourselves to criterion (i) in the present paper we may then say that the problem of calculating technical minimum premiums is broadly spoken equivalent with the problem of estimating loss probabilities. Since an exact calculation of such probabilities is only possible for a few very simple and therefore mostly unrealistic risk models and since e.g. Esscher's method is not always very easy to apply in practice it might be worthwhile to describe in the following an alternative approach using results and techniques from Reliability Theory in order to establish bounds for unknown loss probabilities.

It would have been impossible for me to write this paper without having had the opportunity of numerous discussions with the Reliability experts R. Barlow and F. Proschan while I was at Stanford University. In particular I was told the elegant proof of theorem 3 given below by R. Barlow recently.
A Mutual Reinsurance Scheme
Authors: Bohman Harald , Grenander Ulf
Published: July 2016

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.
Correlations between excess of loss reinsurance covers and reinsurance of the n largest claims baruch berliner
Authors: Berliner Baruch
Published: July 2016

E. Franckx [1] has established the distribution function of the largest individual claim of a portfolio. By assuming the number of claims to be Poisson distributed, H. Ammeter was able to develop the distribution function of the total loss excluding the largest individual claim [2] as well as the distribution function of the nth largest claim [3].

Of course, the nth largest claim is dependent on the largest claim, second largest claim and so on, down to the (nth — 1) largest claim. If we assume the number of claims to be Poisson distributed and the amount of the individual claim to be Pareto distributed, the correlation between the mth largest and the nth largest claim can be expressed by an analytical formula which is susceptible to numerical computation.

With this knowledge we shall be able to compute the variance of the sum of the n largest claims and moreover the correlation between the sum of the n largest claims and the total loss amount. Although an excess of loss reinsurance treaty and a treaty reinsuring the n largest claims are very different in their construction, this paper will show that from a practical point of view there exists a similarity between the two treaties. The correlation coefficient between the sum of the n largest claims and the sum of all claims exceeding a certain limit enables us to assess the degree of similarity.

The correlation coefficient and thus the degree of similarity will prove to be high even in case of the reinsurance of only a small number of largest claims.

Finally, the knowledge of the two first moments of the sum of the n largest claims allows us to compute the premium and the security or variance loading for the reinsurance of the n largest claims.
Some aspects on reinsurance profits and loadings
Authors: Benktander G.
Published: July 2016

In a note on the security loading of excess loss rates I am deducing a simple formula intended to replace some tedious calculations. In the beginning of that note I made the point that some authors recommend a loading proportional to the dispersion of the total claims amount of a treaty δ1 while others tend to favour .

I also stated that a loading proportional to δ1 or its estimate δ1* could be deduced from the statistical uncertainty in measuring the risk (section 4).

The question has been raised if and to what extent a loading system based on the dispersion is unduly punishing the smaller portfolios. This will be examined below.

The pricing concept will be analyzed from the point of view of a big dominating Reinsurer who wants to be fair in all directions. The conclusion of this study supports an affirmative answer to the question put above.

In a second part the loading is studied from a different angle bringing competition into the picture. The pricing or loading becomes a problem of operations research under the simplified assumption that profit is the only purpose of our activity. Not unexpectedly, the loading coming out from this aspect differs from those of part one.

Part two also deals with the question of how much of the loadings which we are aiming for, get lost in the competitive process. It is also shown that in most cases the harder the competition is, the higher loadings shall be used.

Part one and part two thus deal with the loading problem from different aspects, and illustrate the complexity of the problem. It is my hope that this note could stimulate further researches in this interesting and important area, also in a moment when some reinsurers are more concerned with the question of surviving than in fixing the loadings which should on the average and in the long run turn up as profits.
Planning Problems Of A Gambling-House with Application to Insurance Business
Authors: Bohman Harald
Published: July 2016

In the classical risk theory the interdependence between the security loading and the initial risk reserve is studied. It could be said that the purpose of these studies are to state how large the security loading must be in order to avoid ruin of the insurance business. It has often been said that the classical approach with an infinite planning horizon is unrealistic. The main reason for this attitude is that if the security loading is equal to zero then ruin is certain. Since in practice it is often difficult to estimate the true size of the security loading the whole problem of ruin or non-ruin seems to rest on a rather shaky foundation. This attitude to the problem is reflected in studies in risk theory performed in recent years. The infinite planning horizon is then often replaced by a finite time period. Since the probability of ruin during a short period of time depends to a minor extent on the size of the security loading these studies are concentrated mainly on the shape of the claim distribution, while the security loading is of minor interest.

Let us think of a gambling-house, where coin-tossing is practised. Let us assume that the gambling-house for reason of fairness decides to pay two dollars to each winner who has staked one dollar. Probability theory tells us that however rich the gambling-house may be, it will be ruined in the long run. This simple example reminds us of the trivial fact that insurance business without a sufficient security loading in the premium is commercially impossible.
Optimal Insurance Arrangements
Authors: Borch Karl
Published: July 2016

In a recent paper on the theory of demand for insurance Arrow [1] has proved that the optimal policy for an insurance buyer is one which gives complete coverage, beyond a fixed deductible. The result is proved under very general assumptions, but its content can be illustrated by the following simple example.

Assume that a person is exposed to a risk which can cause him a loss x, represented by a stochastic variable with the distribution F(x). Assume further that he by paying the premium P(y) can obtain an insurance contract which will guarantee him a compensation y(x), if his loss amounts to x. The problem of our person is to find the optimal insurance contract, i.e. the optimal function y(x), when the price is given by the functional P(y).

In order to give an operational formulation to the problem we have outlined, we shall assume that the person's attitude to risk can be represented by a Bernoulli utility function u(x), and we shall write S for his “initial wealth”. His problem will then be to maximize

when the functional P(y) is given, and y(x) є Y. The set Y can be interpreted as the set of insurance policies available in the market. It is, natural to assume that o ≤ y(x) ≤ x, but beyond this there is no need for assuming additional restrictions on the set Y.
On the Rating of a Special Stop Loss Cover
Authors: Benktander Gunnar
Published: July 2016

Stop Loss reinsurance has attracted the interest of ASTIN members for years. May I recall the paper of Borch [1] in which he demonstrates some optimality qualities of the stop loss reinsurance from the ceding company's point of view, the contribution of Kahn [2] and the paper of Pesonen [3]. I also mention the paper of Esscher [4] and Verbeek's contribution [5]. Going back to the pre-ASTIN days we find a paper of Dubois [6].

The rating problems have been dealt with by several authors. Let me recall the rating formula worked out by a group of Dutch Actuaries some 20 years ago. This was based on the assumption that the mean and the standard deviation were known. Based on Chebycheff's inequality an approximation formula was worked out which, of course, was heavily on the safe side.

Even younger members of ASTIN are probably familiar with the studies made in the early sixties by a group of Swedish Actuaries, the results of which were presented by Bohman at the Actuarial Congress in London in 1964. Partly based on this, Bühlmann worked out some tables which he used for rating purposes.

My present contribution to the subject may not justify the above reviews, particularly as I will deal with a very special retention situation which a practical underwriter will rightly not accept, namely a stop-loss point as low as equal to the mean value of the distribution.

My excuse for this is that the formula deduced is very handy and that it is of value to the underwriter to know the stop loss risk rate also at this low level.
Compulsory Third Party Insurance: Methods of Making Explicit Allowance for Inflation
Authors: Bruton B. J. , Cumpston J. R.
Published: July 2016

An inflation index is essential when constructing claim payment models from past payment data, and when projecting these results to give estimates of the provisions for outstanding claims and of necessary premiums.

This paper examines the choice of inflation indices for compulsory third party insurance in two Australian states. Two different indices, one based on average weekly earnings per employed male unit and the other based on consumer prices, were tested. The index based on average weekly earnings was considered to be superior in that past claim payment data, together with this index, gave reasonably stable claim payment models.

Some experiments were made for an actual office to illustrate the effects of different inflation rate assumptions.
Study of Factors Influencing the Risk and their Relation to Credibility Theory
Authors: Cabral Maria Amélia , Garcia Jorge Afonso
Published: July 2016

The study and analysis of the various factors influencing insurance risks constitutes an intricate and usually quite extensive problem. We have to consider on the one hand the nature and heterogeneity of the elements we have been able to measure, and on the other the problem of deciding—without knowing exactly what results to expect—on the types of analysis to carry out and the form in which to present the results.

These difficulties, essentially stemming from the fact that we cannot easily define “a priori” a measure of influence, can be overcome only by using highly sophisticated mathematical models. The researcher must define his objectives clearly if he is to avoid spending too much of his time in exploring such models.

Either for these reasons or for lack of our experience in this field we were led to the study of three models, presenting entirely different characteristics though based on the analysis and behaviour of mean value fluctuations, measured by their variances or by the least-squares method.

Our first model, described in II. 1, associates the notion of influence with the notion of variance. It analyses in detail the alteration of the mean values variance, when what we refer to as a “margination” is executed in the parameter space, taking each of the parameters in turn. We start off by having n distinct parameters, reducing them by one with each step.
La Soif du Bonus
Authors: Lemaire Jean
Published: July 2016

In motorcar insurance is widely used a merit rating system characterized by the fact that only the number of claims occurred (and not their amount) modifies the premium. This system induces the insured drivers to support themselves the cost of the cheap claims. We analyze this “hunger for bonus” and solve this decision problem by means of an algorithm related to dynamic programming. The method is then applied to the Belgian bonus system.
Approximations to Risk Theory's F(x, t) by Means of the Gamma Distribution
Authors: Seal Hilary L.
Published: July 2016

It seems that there are people who are prepared to accept what the numerical analyst would regard as a shockingly poor approximation to F (x, t), the distribution function of aggregate claims in the interval of time (o, t), provided it can be quickly produced on a desk or pocket computer with the use of standard statistical tables. The so-called NP (Normal Power) approximation has acquired an undeserved reputation for accuracy among the various possibilities and we propose to show why it should be abandoned in favour of a simple gamma function approximation.

Discounting encomiums on the NP method such as Bühlmann's (1974): “Everybody known to me who has worked with it has been surprised by its unexpectedly good accuracy”, we believe there are only three sources of original published material on the approximation, namely Kauppi et al (1969), Pesonen (1969) and Berger (1972). Only the last two authors calculated values of F(x, t) by the NP method and compared them with “true” four or five decimal values obtained by inverting the characteristic function of F(x, t) on an electronic computer.
Calculation of Ruin Probabilities when the Claim Distribution is Lognormal
Authors: Thorin Olof , Wikstad Nils
Published: July 2016

In this paper some ruin probabilities are calculated for an example of a lognormal claim distribution. For that purpose it is shown that the lognormal distribution function, Λ(y), may be written in the form

where V(x) is absolutely continuous and without being a distribution function preserves some useful properties of such a function.

An attempt is also made to give an approximant Λα(y) to Λ(y) such that Λα(y) is a linear combination of a low number of exponential distributions. For comparison, ruin probabilities are also calculated for two examples of Λα(y).

In the considered numerical cases it is assumed that the occurrence of claims follows a Poisson process.
Calculation of Price Equilibria for Utility Functions of the HARA Class
Authors: Lienhard Markus
Published: July 2016

We explicitly calculate price equilibria for power and logarithmic utility functions which—together with the exponential utility functions—form the so-called HARA (Hyperbolic Absolute Risk Aversion) class.

A price equilibrium is economically admissible in the market which is a closed system. Furthermore it is on the one side individually optimal for each participant of the market (in the sense of maximal expected utility), on the other side it is a Pareto optimum and thus collectively optimal for the market as a whole.