bluuebunny/crossref_metadata_2025 huggingface dataset:
Risk and other factors associated with toxoplasmosis and toxocariasis in pregnant women from southern Brazil
Authors: Santos P.C. , Telmo P.L. , Lehmann L.M. , Mattos G.T. , Klafke G.B. , Lorenzi C. , Hirsch C. , Lemos L. , Berne M.E.A. , Gonçalves C.V. , Scaini C.J.
Published: July 2016

Toxoplasmosis causes complications during pregnancy that have serious effects on fetal development. Thus far, toxocariasis has been reported to spread only via vertical transmission. Nonetheless, the population of pregnant women is also exposed to this infection. Co-infection with bothToxoplasma gondiiandToxocaraspp. has been reported in children, but there are no reports of co-infection in the population of pregnant women. The aim of this study was to determine the prevalence of co-infection withT. gondiiandToxocaraspp. in pregnant women at a university hospital in southern Brazil, and to identify the risk factors associated with infection by both parasites. Two hundred pregnant women were tested for the presence of anti-T. gondiiand anti-Toxocaraspp. antibodies and were asked to complete an epidemiological questionnaire. In this study, the co-infection rate observed in the total population of pregnant women was 8%. In addition, women with a positive result for a serology test forToxocaraspp. were at increased risk of infection byT. gondii(P= 0.019). Co-infection with both parasites in pregnant women was associated with low birth weights in neonates. The similar modes of transmission of both parasites could explain the co-infection. Only a few previous studies have investigated this phenomenon. The findings of the present study emphasize the importance of serological diagnosis during prenatal care and further research in this area to identify risk factors associated with this co-infection, and the possible implications of this co-infection during pregnancy and on the health of newborns.
Bifurcations and symmetry in two optimal formation control problems for mobile robotic systems
Authors: Deng Baoyang , O'Connor Michael , Goodwine Bill
Published: July 2016

This paper studies bifurcations in the solution structure of an optimal control problem for mobile robotic formation control. In particular, this paper studies a group of mobile robots operating in a two-dimensional environment. Each robot has a predefined initial state and final state and we compute an optimal path between the two states for every robot. The path is optimized with respect to two factors, the control effort and the deviation from a desired “formation,” and a bifurcation parameter gives the relative weight given to each factor. Using an asymptotic analysis, we show that for small values of the bifurcation parameter (corresponding to heavily weighting the control effort) a single unique solution is expected, and that as the bifurcation parameter becomes large (corresponding to heavily weighting maintaining the formation) a large number of solutions is expected. Between the asymptotic extremes, a numerical investigation indicates a solution bifurcation structure with a cascade of increasing numbers of solutions, reminiscent, but not the same as, period-doubling bifurcations leading to chaos in dynamical systems. Furthermore, we show that if the system is symmetric, the bifurcation structure possesses symmetries, and also present a symmetry-breaking example of a non-holonomic system. Knowledge and understanding of the existence and structure of bifurcations in the solutions of this type of formation control problem are important for robotics engineers because common optimization approaches based on gradient-descent are only likely to converge to the single nearest solution, and a more global study provides a deeper and more comprehensive understanding of the nature of this important problem in robotics.
Phonological acquisition of Korean consonants in conversational speech produced by young Korean children
Authors: KIM MINJUNG , KIM SOO-JIN , STOEL-GAMMON CAROL
Published: July 2016

This study investigates the phonological acquisition of Korean consonants using conversational speech samples collected from sixty monolingual typically developing Korean children aged two, three, and four years. Phonemic acquisition was examined for syllable-initial and syllable-final consonants. Results showed that Korean children acquired stops and nasals followed by affricates, fricatives, and the liquid. In general, Korean consonants were acquired earlier in syllable-initial position compared to syllable-final position, except for the liquid /l/. The findings are compared with previous research based on single-word assessments, and differences that appear to be associated with the unique morphological system of Korean are noted.
A DSRC Doppler/IMU/GNSS Tightly-coupled Cooperative Positioning Method for Relative Positioning in VANETs
Authors: Shen Feng , Cheong Joon Wayn , Dempster Andrew G.
Published: July 2016

Relative position awareness is a vital premise for the implementation of emerging intelligent transportation systems. However, commercial Global Satellite Navigation Systems (GNSS) receivers do not satisfy the requirements of these applications. Fortunately, Cooperative Positioning (CP) systems, based on inter-vehicle communications, have improved performance of relative positioning in a Vehicular Ad Hoc Network (VANET). CP techniques rely primarily on measurements from the Global Positioning System (GPS) to deliver measurements or positions that describe the location of individual vehicles. In urban environments, the reduced quality or complete unavailability of GPS measurements challenges the effectiveness of any CP algorithm. In this paper, a new enhanced tightly–coupled CP technique is presented by adding the measurements from low-cost inertial sensors and the Doppler shift of the carrier of Dedicated Short-Range Communications (DSRC) signals. In the enhanced CP method proposed here, vehicles communicate their Inertial Measurement Unit (IMU) data and GPS measurements. Each vehicle fuses the GPS measurements and IMU data and the inter-node range-rates based on the Doppler shift of the carrier of DSRC signals. Based on analytical and experimental results, in a full GPS coverage environment, the new tight integration CP outperforms tight CP with Inertial Navigation System (INS), tight CP and differential GPS by at least by 6%, 15%, and 28%, respectively. In a GPS outage, the performance improvement can be up to 60%, 55%, and 66% respectively.
GNSS Jamming Resilience for Close to Shore Navigation in the Northern Sea
Authors: Glomsvoll Oeystein , Bonenberg Lukasz K
Published: July 2016

Navigational error accounts for half of the accidents and serious incidents in close to shore maritime transport in Norway predominantly due to the rapidly changing weather conditions and the dangerous nature of the narrow inshore waters found along the Norwegian coast. This creates a dependence on Differential Global Positioning System (DGPS) use and any disruption to this service can lead to an increased accident rate. The aim of this paper is to research the jamming vulnerability of existing maritime receivers and to understand if an upgrade to a multi-constellation or multi-frequency receiver would improve system resilience. The novelty of this work is a comparison of jamming resilience between different combinations of multiple constellations (GPS and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS)) and multi-frequency Global Navigation Satellite System (GNSS) signals. This paper presents results from GNSS jamming trials conducted in the northern part of Norway, confirming previous research and indicating that typical maritime GPS receivers are easy to jam and may produce erroneous positional information. Results demonstrate that the single frequency multi-constellation receivers offer better jamming resilience than multi-frequency (L1 + L2) GPS receivers. Further, the GLONASS constellation demonstrated a better resilience than GPS. Results demonstrate a known correlation between GPS L1 and L2 frequencies, as well as a probable over-dependence on GPS for signal acquisition, meaning that no signal can be received without GPS L1 present. With these limitations in mind, the authors suggest that the most economic update to the single frequency GPS receivers, currently used for maritime applications, should be multi-constellation GPS + GLONASS receivers. This solution is cheaper and it also offer better jamming resistance for close to shore navigation than dual frequency receivers.
Asymptotic Behaviour of Compound Distributions and Stop-loss Premiums
Authors: Sundt Bjørn
Published: July 2016

The paper gives some asymptotic results for the compound distribution of aggregate claims when the claim number distribution is negative binomial. The case when the claim numbers are geometrically distributed, is treated separately.
The General Economic Premium Principle
Authors: Bühlmann Hans
Published: July 2016

We give an extension of the Economic Premium Principle treated in Astin Bulletin, Volume 11 where only exponential utility functions were admitted. The case of arbitrary risk averse utility functions leads to similar quantitative results. The role of risk aversion in the treatment is essential. It also permits an easy proof for the existence of equilibrium.
On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment
Authors: Reinhard Jean-Marie
Published: July 2016

We consider a risk model in which the claim inter-arrivals and amounts depend on a markovian environment process. Semi-Markov risk models are so introduced in a quite natural way. We derive some quantities of interest for the risk process and obtain a necessary and sufficient condition for the fairness of the risk (positive asymptotic non-ruin probabilities). These probabilities are explicitly calculated in a particular case (two possible states for the environment, exponential claim amounts distributions).
The Influence of Expense Loadings on the Fairness of a Tariff
Authors: Lemaire Jean
Published: July 2016

In non-life insurance, it is nearly always assumed that the expense loading is a fraction of the risk premium. This may deeply affect the fairness of a tariff, as illustrated in the case of the Belgian bonus-malus system.
Détermination de la Fonction de structure d'une classe de Tarif
Authors: D'Hooge L.
Published: July 2016

Le dépouillement statistique d'une classe de tarif hétérogène permet d'observer les fréquences relatives qi des contrats qui pendant une période de référence ont été frappés de (i — 1) sinistres.

On a:

et

Ces fréquences déterminent dans l'espace Rm un vecteur à m composantes, que nous notons:

Une base de décomposition est constituée par un éventail fini de η classes homogènes. Chaque classe homogène Ck est définie par une variable aléatoire, dont la loi de probabilité (λk) dépend du paramètre λk. Théoriquement ce paramètre peut être tout à fait général (un triplet réel p.e.); pour les applications pratiques traitées au paragraphe 4, il suffit pourtant de considérer λk comme un nombre réel.

Si Pi(λk) représente la probabilité à priori d'avoir exactement (i — 1) sinistres dans la classe Ck, nous pouvons noter (λk) par:

(p1(λk), p2(λk), … Pm(λk))

On a:

et

Nous supposons que les vecteurs (λk) sont linéairement indépendants.

Résoudre l'hétérogénéité d'une classe de tarif consiste tout d'abord à choisir une base de décomposition, à représentation analytique connue, et puis à décomposer la classe de tarif par l'éventail des classes homogènes Ck de cette base.
Quadratic Programming in Insurance
Authors: Schmitter H. , Straub E.
Published: July 2016

Abstract and Introduction

Quadratic programming means maximizing or minimizing a quadratic function of one or more variables subject to linear restrictions i.e. linear equations and/or inequalities.

Among the numerous insurance problems which can be formulated as quadratic programs we shall only discuss four, namely the Credibility, Retention, IBNR and the Cost Distribution problems.

Generally, there is no explicite solution to quadratic optimization problems, only statements about the existence of a solution can be made or some algorithm may be recommended in order to get exact or approximate numerical solutions. Restricting ourselves to typical problems of the above mentioned type, however, enables us to give an explicit solution in terms of general formulae for quite a number of cases, such as the onedimensional credibility problem, the retention problem and—under relatively week assumptions— for the IBNR-problem.

The results given here are by no means new. The only goal of this paper is to describe a few fundamental insurance problems from a common mathematical standpoint, namely that of quadratic programming and at the same time, to draw attention to a few special aspects and open questions in this field.
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

The 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

After 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.
Two Pragmatic Approaches to Loglinear Claim Cost Analysis
Authors: ter Berg Peter
Published: July 2016

Parameter estimation in case of loglinear modelled claim cost distribution characteristics is mathematically tractable, especially with the Inverse Gaussian and Lognormal distribution.
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 of

where X1, X2, X3, … are independently and identically distributed random variables with common exponential distribution function

and N is an integer valued random variable with probability function

Then the distribution function of S is given by

If 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 parts

and 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

The 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

In 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 relation

the 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.
Some Problems Connected with the Calculation of Stop Loss Premiums for Large Portfolios
Authors: Esscher Fredrik
Published: July 2016

When experience is insufficient to permit a direct empirical determination of the premium rates of a Stop Loss Cover, we have to fall back upon mathematical models from the theory of probability—especially the collective theory of risk—and upon such assumptions as may be considered reasonable.

The paper deals with some problems connected with such calculations of Stop Loss premiums for a portfolio consisting of non-life insurances. The portfolio was so large that the values of the premium rates and other quantities required could be approximated by their limit values, obtained according to theory when the expected number of claims tends to infinity.

The calculations were based on the following assumptions.

Let F(x, t) denote the probability that the total amount of claims paid during a given period of time is ≤ x when the expected number of claims during the same period increases from o to t. The net premium II (x, t) for a Stop Loss reinsurance covering the amount by which the total amount of claims paid during this period may exceed x, is defined by the formula

and the variance of the amount (z—x) to be paid on account of the Stop Loss Cover, by the formula

As to the distribution function F(x, t) it is assumed that

where

Pn(t) is the probability that n claims have occurred during the given period, when the expected number of claims increases from o to t,

V(x) is the distribution function of the claims, giving the conditioned probability that the amount of a claim is ≤ x when it is known that a claim has occurred, and

Vn*(x) is the nth convolution of the function V(x) with itself.

V(x) is supposed to be normalized so that the mean = I.
Some asymptotic properties of bonus systems
Authors: Loimaranta K.
Published: July 2016

In motorcar insurance—at least in Europe—is widely used a merit rating system called bonus (or malus) system, characterized among others by the fact that only the number of claims occurred does modify the premium. A great variety of different bonus systems is in use. Each country—if not each company—seems to prefer a different bonus system and there is a lack of agreement whether one of them is better than the other. Efforts to construct a theoretically optimal bonus system have not been able to change the situation. General methods to evaluate and compare different existing or proposed bonus systems are therefore wanted.

In the present paper the theory of Markow chains is used to develope formulas for some asymptotic properties of bonus systems. Quantities: efficiency of a bonus system, discrimination power of bonus rules and minimum variance bonus scale are introduced. The last of them gives an asymptotical solution for the problem to find locally “best” bonus scales for given bonus rules. Finally the Danish bonus system is used as an illustration.

We call a merit rating system bonus system if the following assumptions are valid:

i. All policies of a given risk group can be devided into a finite number of classes so that the premium of a policy for a given period depends solely on the class for that period.

ii. The actual class is uniquely defined by the class for the previous period, and the number of claims occurred (regulated) during the period.
Cost Estimates For No-Fault Insurance
Authors: Cumpston J. R.
Published: July 2016

On 12 February 1974, a limited no-fault insurance system was introduced to cover persons killed or injured in road accidents in Victoria, Australia. This system supplements the existing compulsory third party insurance system, under which payments are made only if an insured driver can be shown to be negligent.

The costs of the no-fault benefits are met by compulsory third party insurers, who are allowed to charge not more than the premium fixed by the Government. This paper examines the adequacy of the no-fault component of the premium.

A theoretical model has been developed, covering all the components of compulsory third party and no-fault insurance. This model incorporates the limited available accident and insurance statistics, together with a number of assumptions. As in many practical situations, the limited data available has severely restricted the factors considered, and has reduced the reliability of the estimates made from the model.

The theoretical model does however:

—indicate approximately the premium required for no-fault benefits

—suggest areas where statistical investigation would be valuable

—provide estimates for different types of benefits to different groups of persons, which can be checked as more data becomes available

—provide useful data when considering other forms of no-fault insurance, such as the national rehabilitation and compensation scheme currently being considered by the Australian Government.
Risk-Bearing And Consumption Theory
Authors: Moffet Denis
Published: July 2016

A simple risky situation is studied in the framework of consumption theory. Saving is shown to be a substitute to insurance. Two new concepts, riskbearing budget and effective risk coverage, are introduced in order to give a more accurate insight into the optimal risk-bearing decision. The effect of a variation in current consumption and in wealth upon the optimal insurance coverage is analysed.
Distribution of the Number of Claims in Motor Insurance according to the Lag of Settlement
Authors: Ferrara G. , Quario G.
Published: July 2016

Let Sn be the set of motor claims Si, i = 1, 2, …, N occurred during a given year n, namely Sn represents the set of claims relevant to the generation (or cohort) n.

If Tn is a subset (even empty) of claims resulting without payement (that is the set of zero-claims), the set Pn = Sn − Tn shall denote the set of claims that should be settled.

For every si ∈ Pn, we can define the r.v. Xi which represents the period of time required for its settlement (namely the lag of settlement).

It is not sensible to deem that the r.v. Xi are equally distributed: as a matter of fact we know that the larger is the claim, the longer the lag of payement.

However, we can assume that in a subset U of Pn, the r.v. Xi(U) have the same distribution function, which will be denoted by FU(x) or in short F(x).

As F(x) represents the probability that a claim sj ∈ U is settled within a period o − x, the function 1 − F(x) = l(x) denotes the probability that the claim results unsettled after a lag x, that is the survival function of the claim.

In this study we intend to find an analytical expression of the function 1(x) on the basis of particular assumptions about the behaviour of the adjuster with regard to the settlement of claims.

The assumptions will be tested by fitting the function to some observed data.
A Stop Loss Inequality for Compound Poisson Processes with a Unimodal Claimsize Distribution
Authors: Verbeek H. G.
Published: July 2016

The paper considers the problem of finding an upper bound for the Stop loss premium.

We will start with a brief sketch of the practical context in which this problem is relevant.

If it is reasonable to assume, that the accumulated claims variable of the underlying risk can be represented by a Compound Poisson Process, the following data are needed for fixing the Stop loss premium:

— the claims intensity,

— the distribution of the claimsizes (jump-size variable).

In practical situations it is usually possible to find a reasonable estimate for the claims intensity (expected number of claims in a given period).

Generally speaking, however, it is not so easy to get sufficient data on the claimsize distribution. Ordinarily only its mean is known. This deficiency in information can of course be offset by assuming the unknown distribution to be one of the familiar types, such as Exponential, Gamma or Pareto.

Stop loss premiums are however very sensitive to variations in the type of claimsize distribution and consequently it can make a lot of difference in the result what particular choice is made.

To gain some insight into the consequences of a specific assumption, it is useful to know within what range the premium can move for varying distributional suppositions. This means establishing an upper bound and a lower bound. The lower bound is trivially obtained if the mass of the claimsize distribution is solely concentrated at its mean. The upper bound on the other hand should correspond to the “worst” possible claimsize distribution. This means, that we have to look for a distribution which maximizes the Stop loss premium.
Mixed Compound Poisson Distributions
Authors: Willmot Gord
Published: July 2016

The distribution of total claims payable by an insurer is considered when the frequency of claims is a mixed Poisson random variable. It is shown how in many cases the total claims density can be evaluated numerically using simple recursive formulae (discrete or continuous).

Mixed Poisson distributions often have desirable properties for modelling claim frequencies. For example, they often have thick tails which make them useful for long-tailed data. Also, they may be interpreted as having arisen from a stochastic process. Mixing distributions considered include the inverse Gaussian, beta, uniform, non-central chi-squared, and the generalized inverse Gaussian as well as other more general distributions.

It is also shown how these results may be used to derive computational formulae for the total claims density when the frequency distribution is either from the Neyman class of contagious distributions, or a class of negative binomial mixtures. Also, a computational formula is derived for the probability distribution of the number in the system for the M/G/1 queue with bulk arrivals.
Citizenship, identity and otherness: the orientalisation of immigrants in the contemporary Spanish legal regime
Authors: Barbero Iker
Published: July 2016

Spain is one of the few countries in the EU where Islam has had a historical role in the social and cultural construction of its identity. However, its modern history is marked by acts of repudiation of non-Christian cultures. Opinion polls indicate that certain groups of immigrants from North Africa, Latin America and Eastern Europe, but mainly Muslims, are considered to be incompatible with the popular conception of Spanish identity. The reason for this perception is related to the social construction of the immigrant as the ‘other to govern’ by political, academic and media discourses. The aim of this paper is to demonstrate that immigration law also plays a fundamental role in this strategy of ‘orientalisation’, namely the attribution of certain qualities to immigrant groups (illegal, antisocial, criminal, inassimilable, terrorist), the aim of which is to legitimise the selective control of immigration. The Spanish immigration and citizenship regime contributes to the construction of otherness, and therefore to the political and legal (re)definition of what ‘being Spanish’ means.
A Systematic Review of Global Alpha-Tocopherol Status as Assessed by Nutritional Intake Levels and Blood Serum Concentrations
Authors: Péter Szabolcs , Friedel Angelika , Roos Franz F. , Wyss Adrian , Eggersdorfer Manfred , Hoffmann Kristina , Weber Peter
Published: July 2016

Abstract. The purpose of this study is to systematically review the published literature reporting vitamin E intake levels and serum concentrations in order to obtain a global overview of α-tocopherol status. Articles published between 2000 and 2012 were considered; 176 articles referring to 132 single studies were included. Applying an RDA (recommended daily allowance) of 15 mg/day and EAR (estimated average requirement) of 12 mg/day to all populations with a minimum age of 14 years, 82 and 61 % of mean and median data points were below the RDA and the EAR, respectively. Regarding serum concentrations, globally 13 % of the included data points were below the functional deficiency threshold concentration of 12 µmol/L, mostly for newborns and children. Several prospective observational studies suggest that a serum α-tocopherol concentration of ≥30 µmol/L has beneficial effects on human health. Of the reported study populations and subpopulations, only 21 % reached this threshold globally. This systematic review suggests that the α-tocopherol status is inadequate in a substantial part of the studied populations.