bluuebunny/crossref_metadata_2025 huggingface dataset:
A remark on Wiener process approximation of risk processes
Authors: Grandell Jan
Published: July 2016

In Bohman the following model is considered. Our notation follows Bohman.

Let Z1, Z2, … be a sequence of independent random variables with distribution function F and put

Put

and define X by

X = inf{n; Sn > U, Sk ≤ U for k = 1, …, n − 1}.

Bohman shows that if U → ∞ in such a way that U/σ → ∞ and then

where G(α, x) is the distribution function for the time when a Wiener process X(t) with EX(t) = αt and Var X(t) = t first crosses the level 1.

Let N be an integer, which in a certain sense corresponds to “time”, and consider P(X ≤ N). This is thus the probability of ruin before the N:th claim.
Value and Prices in a Reinsurance Market
Authors: Pressacco Flavio
Published: July 2016

This paper concerns the Borch model of a reinsurance market seen as a model of an economy under uncertainty.

In a market of this type the goods traded are unit coverings contingent to a particular state of nature (n-tuple of claims).

Our idea is to regard the probability of a state of nature as a sort of intrinsic value of the related contingent covering. From this point of view we examine the role of the reinsurance market in modifying values in market equilibrium prices and other questions, related to this classical economic problem, in the particular case of a quadratic utility function for all companies.
On the Numerical Evaluation of Stop-Loss Premiums
Authors: Covens F. , Van Wouwe M. , Goovaerts M.
Published: July 2016

A numerical procedure is described to evaluate the stop-loss premium in case the risk process is a compound Poisson process. The method is mainly based on an algorithm of R. Piessens and M. Branders for the numerical evaluation of Fourier transforms.
Modèles Additifs et Non Additifs en Actuariat
Authors: Vincke Philippe
Published: July 2016

De nombreux modèles, en actuariat, se basent sur l'existence d'une fonction d'utilité additive. Le but de cet article est de montrer que cette hypothèse enlève au problème traité son caractère dynamique et que la suppression de l'additivité conduit à une solution plus réaliste.
Étude Statistique de la Probabilité de Sinistre en Assurance Automobile
Authors: Hallin Marc , Ingenbleek Jean-François
Published: July 2016

Dans trois études récentes (1977a, 1977b, 1979), J. Lemaire a appliqué à un ensemble d'observations du risque automobile quelques méthodes de sélection fréquemment utilisées en analyse de la régression. Les variables explicatives (traitées comme variables indépendantes) sont les variables décrivant le risque. Les variables étudiées (traitées comme variables dépendantes d'un modèle de régression) sont les deux variables généralement prises en considération dans ce contexte: le nombre des sinistres et leur montant cumulé.

Nous avons déjà souligné (Hallin, 1977) combien les hypothèses qui se trouvent à la base de l'analyse de la régression — normalité, homoscédasticité et linéarité de la régression — sont loin d'être remplies dans le contexte de l'assurance automobile. Le montant cumulé annuel prend la valeur zéro avec une probabilité proche de 0.9! Le nombre annuel de sinistres vaut 0, 1, 2, rarement plus! Même très approximativement, de telles variables peuvent difficilement être considérées comme normales. En outre, la plupart des variables explicatives sont de type nominal ou ordinal, ce qui rend délicate l'utilisation de modèles linéaires, les interactions de tous ordres étant très importantes, ainsi qu'on pourra le constater. Ces réserves sont d'ailleurs prévues par Jean Lemaire lui-même, qui ne propose ses conclusions qu'à titre de première approximation. Les mêmes données ont encore été soumises (Masure, 1978) aux méthodes de l'analyse discriminante, et les mêmes réserves peuvent être faites en ce qui concerne l‘utilisation des méthodes et l'interprétation des résultats (combinaisons linéaires, etc.).

Nous avons proposé dans Hallin (1977a, b) un ensemble de méthodes qui, selon les hypothèses distributionnelles pouvant être faites (et qui vont des hypothèses classiques de l'analyse de la variance à celles, beaucoup moins restrictives, des méthodes de rangs), constituent des généralisations de celles qui sont utilisées par Jean Lemaire. En particulier, celle que nous appliquons ici est entièrement “distribution free”. Ces méthodes sont également une extension de celle qu'a proposée Pitkänen (1975, 1976).
Rating of Largest Claims and Ecomor Reinsurance Treaties for Large Portfolios
Authors: Kremer Erhard
Published: July 2016

In the present paper we deal with the problem of calculating a premium for the largest claims and ECOMOR reinsurance treaties. Ammeter derived already in 1964 formulas for calculating the premiums of the largest claims and ECOMOR reinsurance treaties (compare also Seal (1969), Thépaut (1950)), which we will restate in the following Section 2. Lately Benktander (1978) has established an interesting connection between the premiums of the largest claims and excess of loss reinsurance treaties. He proved that the net risk premium of the largest claims treaty covering theplargest claims is bounded by the risk premium of an excess of loss treaty plusptimes its priority, which has to be determined such that the mean number of excess claims equalsp.Furthermore Benktander showed in examples that the upper bound is quite good in case of the Poisson-Pareto risk process. Nevertheless he did not give a formal proof for the quality of the bound in the Poisson-Pareto case nor for other risk processes.

In the following note we take up this last point and prove that for general risk process Benktander's upper bound is equivalent to the premium of the largest claims reinsurance cover when the size of the collective approaches infinity. Consequently, for large portfolios the risk premium of the largest claims cover may be replaced by the upper bound, e.i., calculated from the premium of the corresponding excess of loss treaty. Moreover we state a similar result for the ECOMOR treaty.
Assurance Automobiles — Statistique et tarifs
Authors: Cannet Alexandre
Published: July 2016

Commentaires sur les constatations expérimentales d'une Compagnie Française en matière d'Assurance Responsabilité Civile Automobile pour la période de 1949 à 1959 et méthode préconisée pour la détermination du prix de revient moyen d'une catégorie de risques bien définie.

De nombreux travaux actuariels ou statistiques ont été effectués dans tous les pays pour rechercher les lois pouvant régir les primes d'assurance Automobile en fonction de certaines variables.

Il ne semble pas toutefois que ces travaux théoriques soient facilement exploitables dans la pratique, étant donné les difficultés de saisir d'une manière suffisamment approchée les valeurs réelles des variables.

Notamment, en matière d'assurance Responsabilité Civile Automobile, l'expérience française montre que dans les éléments pouvant servir au calcul des primes, seul parait suffisamment connu à ce jour, le nombre des véhicules exposés au risque.

Dans une Conférence faite à l'Institut des Actuaires Français M. Constant a exposé ses recherches d'une loi de distribution permettant de déterminer les variations du coût moyen des sinistres en fonction des variations d'indices économiques, mais il ne semble pas qu'une utilisation pratique de cette théorie ait pu être obtenue dans le cadre des Entreprises d'Assurances Françaises.

C'est pourquoi il m'a paru bon d'exposer ci-après les résultats d'une méthode expérimentale utilisée dans une importante Compagnie d'Assurance Française pour apprécier si des corrélations peuvent apparaître entre la variation du coût moyen des sinistres et la variation du ou de plusieurs indices économiques. Cette méthode par ailleurs, donne également un moyen pour déterminer un nombre théorique de sinistres qui soit à l'abri des modifications importantes que les déclarations de sinistres — seul élément connu dans les Compagnies — peuvent subir selon certaines conjonctures.
Approximations of the generalised Poisson function
Authors: Kauppi Lauri , Ojantakanen Pertti
Published: July 2016

One of the basic functions of risk theory is the so-called generalised Poisson function F(x), which gives the probability that the total amount of claims ξ does not exceed some given limit x during a year (or during some other fixed time period). For F(x) is obtained the well known expansion

where n is the expected number of claims during this time period and Sk*(x) is the k:th convolution of the distribution function S(z) of the size of one claim. The formula (1) is, however, much too inconvenient for numerical computations and for most other applications. One of the main problems of risk theory, which is still partly open, is to find suitable methods to compute, or at least to approximate, the generalised Poisson function.

A frequently used approximation is to replace F(x) by the normal distribution function having the same mean and standard deviation as F as follows:

where α1 and α2 are the first zero-moments of S(z):

SM(Z) is here again the distribution function of the size of one claim. To obtain more general results a reinsurance arrangement is assumed under which the maximum net retention is M. Hence the portfolio on the company's own retention is considered. If the reinsurance is of Excess of Loss type, then

where S(z) is the distribution function of the size of one total claim.
Procedures and basic statistics to be used in magnitude control of equalisation reserves in Finland
Authors: Hovinen Esa
Published: July 2016

This report aims at describing the procedures and statistics prepared for use in calculation of the limits of the equalisation reserves of Finnish insurance companies. The report is based on work done by a committee which the Federation of Finnish Insurance Companies set up in 1962. Its purpose was to collect and work up the necessary statistics and to develop computational methods to be used in practice for the computation of equalisation reserves. In one respect the work was initiated by the Supervisory Service, which prepared new and more precise regulations concerning the determination of limits of the above reserves.

Because solvency problems of insurance companies have had great attention in recent years internationally, and the Finnish equalisation reserves are closely related to them, the theme may be sufficiently interesting to be presented once more setting out practical results. The solvency problem among other questions has been dealt with by Drs. Pesonen and Pentikäinen in former colloquia. This report can be considered as a continuation of Dr. Pesonen's paper “Magnitude Control of Technical Reserves in Finland” submitted to the Lucerne Colloquium and my paper “A Procedure to Compute Values of the Generalised Poisson Function” to the same colloquium.

The principles and theoretical formulae to be used in computation of the limits for the equalisation reserves have already been stated in the papers of Drs. Pesonen and Pentikainen. Other technical reserves are not dealt with here.

The equalisation reserve is roughly defined as that part of the technical reserves which exceeds the conventional premium reserve and the claims reserve and which secures the company's solvability against random fluctuations of claims and fluctuation of the basic probabilities of the claims. The equalisation reserve E must be greater than a minimum Emin from solvability reasons and, because of taxation, should not exceed a maximum amount Emax.
Comments on different deductions of expressions for conditional expectations
Authors: Philipson Carl
Published: July 2016

1. In a paper presented to the fifth Astin Colloquium (Lucerne, 1965) Bühlmann has given some propositions with regard to Experience Rating understood as a sequence of estimates of the expectation with respect to the distribution function of θ, H(θ) say, of μ(θ) which is the mean for fixed θ with respect to the distribution function G(x; θ) of the variables for each value of ν = 1, 2 … n. In such problems the estimator function for μ(θ) is generally chosen to be the conditional mean of μ(θ) for a given set of observed values of This is generally justified by the principle of least square deviation. According to Bühlmann this justification is not sufficient. Therefore, he bases the choice of this estimator function upon a postulate of equilibrium, described in the following lines.

Let X′ be a subset of X, and C(X′) a cylinder with the base X′ ⊂ X in the product space X × Θ, where X is the set of all possible and Θ the set of all possible θ, then the postulate of equilibrium implies the equality between the expectations of μ(θ) and of a function of on each cylinder C(X′). This is exactly Kolmogoroff's definition of the conditional expectation:

Bühlmann states, further, that the best linear estimate of (1) based on the arithmetic mean of n sample values xν of ν = 1, 2 … n can be written in the form of the Credibility Formula:

where the symbol E[·] denotes the expectation over the product space X × Θ and

If the are independent and identically distributed, this leads to where k = E [σ2 (θ)] / Var [ν(θ)], and σ2(θ) is the variance for a fixed θ of G(x; θ). This case of the credibility formula is, generally, applied in American practice. (The proposition has later been proved for more general conditions).
An analysis of the development of the fire losses in the northern countries after the Second World War
Authors: Andersson Hans
Published: July 2016

In several different countries there has lately been a very unfavourable development as far as fire losses are concerned. There have been many and very bad big fires which have especially affected industry and trade. The facts which can be considered to have caused this development are well-known. Bigger and bigger and more concentrated units of production, business enterprises, and storing form an accumulation of values which in itself implies increasing risks. On account of production-technical and business-economical conditions it has not always been possible to divide the buildings into sections desirable from a fire service point of view. The new production methods have sometimes caused new fire risks.

The Northern Central Office for Fire Insurance Statistics from Mutual Companies (CNÖB) has made an investigation in order to see to what extent the international trend towards increasing fire losses has any equivalence in the Northern countries (Denmark, Finland, Norway, and Sweden). I.a. there was made a graphical representation of how the observed rate of net risk premium of the portfolio has developed during the period 1946–1966, the result of which may be seen from fig. 1. No increasing trend can be observed from this. After having been decreasing during the immediate postwar time, the observed rate of net risk premium has been fairly constant from the beginning of the fifties, perhaps even somewhat decreasing except during the later years. The conclusion is that in so far facts as mentioned above have influenced the development of claims of the portfolios or parts of these in a deteriorating way, there must in that case have been circumstances which have worked as neutralizers.
Distributions des sinistres incendie selon leur coût
Authors: Ferrara Giovanna
Published: July 2016

On peut penser que la dimension des sinistres est la résultante d'un très grand nombre de causes indépendantes à effets positifs.

Soient

les variables aléatoires indépendantes qui représentent les facteurs élémentaires exerçant leur action dans l'ordre indiqué par les indices.

Si Xν est l'ampleur du sinistre dû aux facteurs ξ1, ξ2, …., ξν nous pouvons supposer que l'augmentation causée par ξν+1 soit proportionelle à ξν+1 et à une certaine fonction, g(Xν) de la dimension Xν.

C'est à dire, nous supposons qu'il y ait les relations:

Si chaque facteur n'apporte qu'un faible contribut à l'augmentation du sinistre, nous pouvons alors poser approximativement aussi:

Comme X varie de Xo à Xn (et que X = Xn désigne la dimension extrème du sinistre) le second membre de la (2) décrit une variable aléatoire, fonction de X.

Puisque par hypothèse ξ1,, ξ2, …., ξn sont des variables aléatoires indépendante, si n est suffisament grand, d'après le théorème de la limite des probabilités il s'insuit que la variable aléatoire au second membre de la (2), est, à la limite, distribuée suivant la loi normale. Si l'on pose g(t) = t − c, la variable aléatoire normale qui décrit la dimension du sinistre pourra être posée dans la forme In(X − c).
On Optimal Reinsurance
Authors: Verbeek H. G.
Published: July 2016

In this paper an attempt is made to find an answer to the question, “What is the most advantageous size for the retention limit of a risk portfolio, given the fact that a certain stability requirement is to be satisfied?”

This problem will be approached from the viewpoint of an insurer who wishes to obtain a certain degree of stability at lowest cost.

It is assumed that in his choice of reinsurance methods, the insurer restricts himself to either a surplus treaty, a stop loss treaty or a combination of both these types.

Moreover it is assumed that “stability” can be adequately measured by the variance of the risks retained for own account.

We start to consider a reinsurance policy based on the surplus system where the amount of risk in excess of a retention limit u is ceded.

By thus limiting the potential loss on each risk individually, the variance is kept at a certain level, but at the expense of an amount of premium payable to a reinsurer.

The insurer could, of course, reduce the reinsurance cost by increasing his retention but he then is bound to incur a higher variance in his portfolio, which would mean a loss of stability.

One might ask, however, whether a suitably chosen stop loss coverage could bring the variance down again to the proper level at lesser cost than the profit obtained by taking a higher retention. A reduction in reinsurance cost would then have been effected.

The question leads to an optimization problem, which in a more general setting, has been discussed by K. Borch.
Markov chains and the determination of fair premiums
Authors: Vajda Stefan
Published: July 2016

The relationships between actuarial and pure mathematics are curious. Actuaries have contributed to the development of mathematical theory: it is sufficient to mention, as examples, Fredholm of an earlier, and Cramér of a more recent generation. Scandinavian mathematicians, in particular, have been concerned with a very special type of stochastic process, reflected in the collective theory of risk, and the work of Philipson, Ammeter and others in this field is well known to readers of this Bulletin. However, the main stream of the theory of stochastic processes has little contact with actuarial applications.

On the other hand, many actuaries have studied and assimilated pure mathematics and have thrown light on actuarial matters by describing their own preoccupations in the terminology of modern, often abstract, mathematics. E. Franckx is one of their number.

The Instituto di Matematica Finanziaria of the University of Trieste (Faculty of Economics and Commerce) has published a booklet entitled

Essai d'une théorie opérationnelle des risques Markoviens which contains three lectures delivered by Professor Franckx in Trieste and a contribution which he presented to the 17th Congress of Actuaries, held in London in 1964.
Tariff Theory
Authors: Pitkänen Paavo
Published: July 2016

When an insurance company accepts new insurances or when the premiums of earlier accepted insurances have to be changed on renewal the company has to

— search for the factors that influence the premium and

— calculate the premium according to the values of these factors.

In order to calculate the premiums the company gathers data consisting of factors eventually influencing the amount of claims. On the basis of these data the company calculates the tariff which has to fulfill the following general principles:

1. The tariff has to be as correct as possible in relation to different risk groups.

2. The structure of the tariff has to be such that the calculation of the insurance premium is quite straightforward. With this in mind the factors influencing the tariff have to be few enough and the structure of the tariff has to be the simple (e.g. linear or multiplicative) function of the factors or it should be rather easy to put them into tabular form.

These principles are partly contradictory. If the premium is correct, the structure of the tariff is not usually simple.
Representations of Claims Arising From A Risk Portfolio
Authors: Reid D. H.
Published: July 2016

This paper is concerned with certain problems which arise in the course of rate fixing for a portfolio comprising a large number of direct risks.

This is, of course, the traditional territory of the actuary and there is no lack of papers discussing specific aspects of the subject, such as the analysis of claim frequency, or the fitting of distributions to claim amount data. Equally there is a literature which discusses in general terms the philosophy which it is suggested should be followed by the non-life insurance ratemaker. It is when one tries in practice to follow a logical and consistent path through from portfolio records to rates that gaps in the literature become apparent and it is with covering these gaps, or at least some of them, that the present paper is concerned.

It is not the concern of the author in this paper to attempt to describe the entire ratemaking process. That there is no reference to the analysis of office expenses, commissions, or to the application of “judgment” or “experience” should not be taken to imply that these aspects are not susceptible to the kind of approach advocated here. Attention here is focused upon what might in a sense be regarded as the most basic aspect: the claim process or experience.

In many insurance operations the position which seems to be developing is that there is no lack of necessary computer hardware, and in principle, of data: the difficulties arising relate more to the form in which data should be retained and extracted, and the manner in which it should be used to assist in rate-making.
How To Find The Right Subdivision Into Tariff Classes
Authors: Schmitter H. , Straub E.
Published: July 2016

By intuition, the subdivision of an insurance portfolio into a number of classes is said to be good if it reflects the heterogeneity of the portfolio in an efficient way. To illustrate this rather vague statement we take the following very simple example:

The portfolio consists of 20 independent risks, 10 of them producing an expected loss ratio of say 30% each (type A risks) and 80% each (type B risks) respectively.

This “natural” subdivision is certainly better than, for instance, no subdivision at all;

or, the finest possible subdivision with 20 classes consisting of only 1 risk each (because there is no point in differentiating between risks of the same type);

or, 5 classes each containing two A- and two B-risks (here the number of classes is unnecessarily high and the heterogeneity has been completely wiped out; statistics based on this subdivision would even make us believe that the portfolio is totally homogeneous).

As a matter of fact, the above “natural” subdivision is—of course!—the best of all subdivisions, it is the optimal subdivision in this case.

In practice, however, as we all know, it is not easy to find the optimal subdivision. For one thing, the inherent structure or “natural” subdivision is not known a priori and secondly, for many different reasons, we can only choose from a limited number of subdivisions and not from all theoretically possible solutions. Note that even with only 20 risks there are 58.1012 possibilities of subdividing the portfolio. Thus, in practice, there is only a relatively small number of admissible subdivisions and the optimal one may not be among them, but we still need some sort of statistical criterion to choose the best one from these admissible subdivisions.
The Harald Cramér Volume
Authors: Philipson Carl
Published: July 2016

Harald Cramér was nominated Professor in Actuarial Mathematics and Mathematical Statistics at the University of Stockholm in the late twenties. 1959 a book was “dedicated to Harald Cramér on his sixty-fifth birthday, in recognition of his pathbreaking work in probability and statistics”, with the title Probability and Statistics, The Harald Cramér Volume (Almqvist & Wiksell, Uppsala 1959; John Wiley & Sons, New York). The development during these three decades can be described in Cramér's own words in a recently published „Éloge de M. Paul Lévy.” “Pendant ces années” (the late twenties) “la théorie moderne des probabilités a commencé ce développement puissant qui, depuis cette époque, a continué sans cesse, et qui a fait de la théorie des probabilités une des branches les plus fécondes de l'analyse moderne, ayant les rapports intimes avec tous les domaines des mathématiques pures, et en même temps des applications pratiques dont l'étendue et l'importance vont toujours en croissant.”

A few historical notes will be given as a background for the review of The. Harald Cramér Volume, 1903-1934 Filip Lundberg formed the collective theory of risk. This theory is a particular part of the general theory of stochastic processes which latter was drafted, in its main lines, by Kolmogoroff, 1931 and 1933. (A stochastic process is constituted by a variable depending on chance which is simultaneously a function of one or more variates. For readers not used to this terminology such a variable may be exemplified with the total risk costs for a certain period paid for a group of policies issued by a fire insurance company. For simplicity, it is assumed that the group involves only agricultural risks, similar to each other and situated in the open country so that no conflagration can occur. Further we assume that during the period of observation no change occurs in the composition of the group neither through underwriting, nor through cancellation, nor through alteration.
Sur la Combinaison des evenements et les resultats aleatoires quantitatifs qui en resultent
Authors: Franckx
Published: July 2016

1.1. — Le titre de cette note indique que le problème étudié est très général et par le fait même applicable à de nombreux domaines; physique, biologie, recherche opérationnelle, assurances, téléphonie, etc …

C'est évidemment parce que certains problèmes ont la même structure que leur considération sous forme abstraite, est plus importante. C'est la raison pour laquelle nous traitons le problème de structure, qu'il suffit de particulariser dans chaque domaine d'application.

a) Nous supposerons une période de référence de durée constante.

b) Un évènement E, généralement quelconque, mais invariable, peut se produire pendant cette période. Le nombre de fois que cet évènement se réalise est une variable aléatoire I, qui sera définie par la suite

qi désignant la probabilité pour que E se réalise i fois pendant la période de référence. Nous conviendrons de dire que I mesure l' “intensite” du phénomène E.

c) Lorsque l'évènement E se réalise, on effectue une expérience relativement à. une autre variable aléatoire quantitative N (positive ou non). Cette variable stochastique est completement définie par sa fonction de répartition.

F(n) = prob{N<n}

généralement quelconque; nous conviendrons de dire que n est le “niveau” atteint par la variable N au cours de l'expérience.

1.3. — De nombreux problèmes de la vie courante peuvent être synthétisés sous cette forme et pour ne mentionner que quelques dans le domaine de la vie des organismes d'assurances, citons sous forme de tableau

Cette simple énumération indique la grande variété de problèmes de même structure que l'on rencontre journellement; il est par suite utile de les traiter en synthèse.
Colloque Astin 1963 de Trieste Rapport introductif sur le 2e thème, partie a
Authors: Thyrion P.
Published: July 2016

Le “Contrôle actuariel dans la comptabilité des branches élémentaires” constitue le 2e thème de ce colloque, tel que l'annonce le programme officiel. Ce thème comprend une ière partie intitulée: “Problèmes relatifs aux sinistres”, qui est le sujet de cette séance.

Les notes préliminaires de notre Président, parues dans notre dernier bulletin, suggéraient d'orienter les travaux vers les applications pratiques de l'important travail théorique déjà réalisé dans le cadre d'Astin. Plus particulièrement en ce qui concerne les sinistres dans les assurances de responsabilité civile, ces notes attiraient l'attention sur une certaine analogie que la longue dureé de règlement des sinistres pouvait créer entre l'estimation des réserves pour sinistres à régler et l'évaluation des réserves mathématiques en branche Vie et elles soulevaient dès lors assez naturellement la question des méthodes d'estimation collective. En fait, les communications qui ont été rattachèes à cette rère partie du 2e thème interprètent le sujet de manière extrêmement large. Ne voyez dans cette réflexion initiale nul reproche aux auteurs, mais la simple constatation d'un fait dont mon rapport introductif doit tenir compte: il ne sera pas une synthese dans les directions proposées par notre Président.

Une partie des communications se rattache au fond à la théiorie du risque. Pour mieux dégager l'apport de ces notes, je me propose de le dépouiller autant que possible de son aspect purement mathématique et de le situer dans l'évolution des idées et des recherches en la matière.

J'indiquerai ensuite l'apport des communications au sujet de l'estimation des réserves pour sinistres à régler.

Enfin, je résumerai les travaux qui se rapportent à la tarification du risque automobile.
A Short Note on Overall Risk Management in an Insurance Concern
Authors: Borch Karl
Published: July 2016

1. At an earlier ASTIN Colloquium participants were invited to present notes on problems which they considered as important but unsolved. There was little response to this invitation, presumably because a problem, once it is well formulated, is almost solved.

In this Note I do not present any new problems. In stead I try to outline a framework which may be useful for analysing different risk problems and seeing them in their proper perspective. In my view, a framework of this kind is urgently needed to place today's actuarial work on a sound foundation.

2. In general an insurance contract will define two stochastic processes. We lose little by assuming that the processes are discrete, and describing them in the following manner:

(i)The payment process:x0,x1…xt…, wherextis the amount which the company pays to settle claims in periodt, or at timet.

(ii)The premium process:p0,p1…pt…, where pt is the premium which the company receives in periodt, or at timet.

If the contract is concluded at timet= o, thePrinciple of Equivalencerequires that

For the typical short-term contract with premium payable in advance (i) will reduce to

3. For a long-term insurance contract one usually requires that the inequality

shall hold for all τ. This means that the company must never be a net creditor of its customer.
Regularity Conditions For Exact Credibility
Authors: Jewell William S.
Published: July 2016

Conditions under which the natural conjugate prior is not zero on its boundary are given, correcting an argument about conditions for exact credibility given in another paper.
Statistical Methodology for Large Claims
Authors: de Oliveira J. Tiago
Published: July 2016

The question of large claims in insurance is, evidently, a very important one, chiefly if we consider it in relation with reinsurance. To a statistician it seems that it can be approached, essentially, in two different ways.

The first one can be the study of overpassing of a large bound, considered to be a critical one. If N(t) is the Poisson process of events (claims) of intensity v, each claim having amounts Yi, independent and identically distributed with distribution function F(x), the compound Poisson process

where a denotes the critical level, can describe the behaviour of some problems connected with the overpassing of the critical level. For instance, if h(Y, a) = H(Y − a), where H(x) denotes the Heavside jump function (H(x) = o if x < o, H(x) = 1 if x ≥ o), M(t) is then the number of claims overpassing a; if h(Y, a) = Y H(Y − a), M(t) denotes the total amount of claims exceeding the critical level; if h(Y, a) = (Y − a) H(Y − a), M(t) denotes the total claims reinsured for some reinsurance policy, etc.

Taking the year as unit of time, the random variables M(1), M(2) − M(1), … are evidently independent and identically distributed; its distribution function is easy to obtain through the computation of the characteristic function of M(1). For details see Parzen (1964) and the papers on The ASTIN Bulletin on compound processes; for the use of distribution functions F(x), it seems that the ones developed recently by Pickands III (1975) can be useful, as they are, in some way, pre-asymptotic forms associated with tails, leading easily to the asymptotic distributions of extremes.
Estimation and Testing for Functional Form in Pure Premium Regression Models
Authors: Harrington Scott E.
Published: July 2016

Estimation of pure premiums for alternative rate classes using regression methods requires the choice of a functional form for the statistical model. Common choices include linear and log-linear models. This paper considers maximum likelihood estimation and testing for functional form using the power transformation suggested by Box and Cox. The linear and log-linear models are special cases of this transformation. Application of the procedure is illustrated using auto insurance claims data from the state of Massachusetts and from the United Kingdom. The predictive accuracy of the method compares favorably to that for the linear and log-linear models for both data sets.
An Essay at Measuring the Variance of Estimates of Outstanding Claim Payments
Authors: Ashe Frank
Published: July 2016

The variance of statistical estimates of outstanding claim payments for long-tailed general insurance portfolios is examined. The variance's three components are discussed. As there is no accepted technique for measuring this variance three methods are investigated empirically for its measurement—a parametric method, the jackknife method, and the bootstrap method. No method stands out as superior to the others and it is recommended that all three be evaluated and used to gauge the possible errors in the estimation of outstanding claims.
A MISFIT IN ALL TIMES: H. G. WELLS AND “THE LAST WAR”
Authors: NORDLUND ALEXANDER M.
Published: July 2016

The First World War is often alluded to as “the war to end all wars,” a phrase credited to H. G. Wells at the outbreak of the conflict. Rather than a self-proclaimed product of war enthusiasm in 1914, his declaration represented a consistent vision of warfare that Wells circulated in much of his work: that a major war would cause the collapse of the nation state and facilitate the rise of a utopian, technocratic world state. Although partly a cultural product of his own times, Wells mythologized himself as a misfit in all times: a sociopolitical critic antithetical to the madness of his own society. This study asserts that rather than an attempt at prophecy, it is this misfit image that informed his declaration in 1914 and societal responses to it.
Transitions in a genetic transcriptional regulatory system under Lévy motion
Authors: Zheng Yayun , Serdukova Larissa , Duan Jinqiao , Kurths Jürgen
Published: July 2016

Based on a stochastic differential equation model for a single genetic regulatory system, we examine the dynamical effects of noisy fluctuations, arising in the synthesis reaction, on the evolution of the transcription factor activator in terms of its concentration. The fluctuations are modeled by Brownian motion and α-stable Lévy motion. Two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), are used to analyse the transitions from the low to high concentration states. A shorter MFET or higher FEP in the low concentration region facilitates such a transition. We have observed that higher noise intensities and larger jumps of the Lévy motion shortens the MFET and thus benefits transitions. The Lévy motion activates a transition from the low concentration region to the non-adjacent high concentration region, while Brownian motion can not induce this phenomenon. There are optimal proportions of Gaussian and non-Gaussian noises, which maximise the quantities MFET and FEP for each concentration, when the total sum of noise intensities are kept constant. Because a weaker stability indicates a higher transition probability, a new geometric concept is introduced to quantify the basin stability of the low concentration region, characterised by the escaping behaviour.
A composite light-harvesting layer from photoactive polymer and halide perovskite for planar heterojunction solar cells
Authors: Wang Heming , Rahaq Yaqub , Kumar Vikas
Published: July 2016

A new route for fabrication of photoactive materials in organic-inorganic hybrid solar cells is presented in this report. Photoactive materials by blending a semiconductive conjugated polymer with an organolead halide perovskite were fabricated for the first time. The composite active layer was then used to make planar heterojunction solar cells with the PCBM film as the electron-acceptor. Photovoltaic performance of solar cells was investigated by J-V curves and external quantum efficiency spectra. We demonstrated that the incorporation of the conjugated photoactive polymer into organolead halide perovskites did not only contribute to the generation of charges, but also enhance stability of solar cells by providing a barrier protection to halide perovskites. It is expected that versatile of conjugated semi-conductive polymers and halide perovskites in photoactive properties enables to create various combinations, forming composites with advantages offered by both types of photoactive materials.
N-terminal pro b-type natriuretic peptide (NT-pro-BNP) –based score can predict in-hospital mortality in patients with heart failure
Authors: Huang Ya-Ting , Tseng Yuan-Teng , Chu Tung-Wei , Chen John , Lai Min-Yu , Tang Woung-Ru , Shiao Chih-Chung
Published: July 2016

Serum N-terminal pro b-type natriuretic peptide (NT-pro-BNP) testing is recommended in the patients with heart failure (HF). We hypothesized that NT-pro-BNP, in combination with other clinical factors in terms of a novel NT-pro BNP-based score, may provide even better predictive power for in-hospital mortality among patients with HF. A retrospective study enrolled adult patients with hospitalization-requiring HF who fulfilled the predefined criteria during the period from January 2011 to December 2013. We proposed a novel scoring system consisting of several independent predictors including NT-pro-BNP for predicting in-hospital mortality, and then compared the prognosis-predictive power of the novel NT-pro BNP-based score with other prognosis-predictive scores. A total of 269 patients were enrolled in the current study. Factors such as “serum NT-pro-BNP level above 8100 mg/dl,” “age above 79 years,” “without taking angiotensin converting enzyme inhibitors/angiotensin receptor blocker,” “without taking beta-blocker,” “without taking loop diuretics,” “with mechanical ventilator support,” “with non-invasive ventilator support,” “with vasopressors use,” and “experience of cardio-pulmonary resuscitation” were found as independent predictors. A novel NT-pro BNP-based score composed of these risk factors was proposed with excellent predictability for in-hospital mortality. The proposed novel NT-pro BNP-based score was extremely effective in predicting in-hospital mortality in HF patients.
High-quality III-nitride films on conductive, transparent (2̅01)-oriented β-Ga2O3 using a GaN buffer layer
Authors: Muhammed M. M. , Roldan M. A. , Yamashita Y. , Sahonta S.-L. , Ajia I. A. , Iizuka K. , Kuramata A. , Humphreys C. J. , Roqan I. S.
Published: July 2016

We demonstrate the high structural and optical properties of InxGa1−xN epilayers (0 ≤ x ≤ 23) grown on conductive and transparent ("Equation missing"01)-oriented β-Ga2O3 substrates using a low-temperature GaN buffer layer rather than AlN buffer layer, which enhances the quality and stability of the crystals compared to those grown on (100)-oriented β-Ga2O3. Raman maps show that the 2″ wafer is relaxed and uniform. Transmission electron microscopy (TEM) reveals that the dislocation density reduces considerably (~4.8 × 107 cm−2) at the grain centers. High-resolution TEM analysis demonstrates that most dislocations emerge at an angle with respect to the c-axis, whereas dislocations of the opposite phase form a loop and annihilate each other. The dislocation behavior is due to irregular ("Equation missing"01) β-Ga2O3 surface at the interface and distorted buffer layer, followed by relaxed GaN epilayer. Photoluminescence results confirm high optical quality and time-resolved spectroscopy shows that the recombination is governed by bound excitons. We find that a low root-mean-square average (≤1.5 nm) of InxGa1−xN epilayers can be achieved with high optical quality of InxGa1−xN epilayers. We reveal that ("Equation missing"01)-oriented β-Ga2O3 substrate has a strong potential for use in large-scale high-quality vertical light emitting device design.
Polyacrylates for Personal Care
Authors: Wiyanto Ivan , Loh Xian Jun
Published: July 2016

Polymers have been used extensively in personal care products. The polymers used in personal care products range from both synthetic and natural polymers. The high demand for using polymers in personal care products is mainly because it is easy to obtain various final performance product attributes just by altering the structures and properties of the polymers. One of the polymers used in personal care products is polyacrylates. The term “acrylates” is defined as non-cross-linked copolymers containing a combination of acrylic acid, methacrylic acid and their simple esters. Polyacrylates in personal care products play important roles as thickeners, rheological modifiers, media for delivery of active ingredients, film formers, emulsifiers, moisturisers, dispersants, waterproofers and conditioners. Their key functionalities include the ability to increase the viscosity of solutions, form physical gels, stabilise dispersions and emulsions, induce particle aggregation, solubilise hydrophobic compounds, modify surface properties and facilitate the controlled release of active compounds.
Natural Rheological Modifiers for Personal Care
Authors: Zheng Yujie Jason , Loh Xian Jun
Published: July 2016

The development of personal care formulations incorporates the deliberation of the prerequisite product rheology and the right rheology modifier to deliver these effects. While the effectiveness of the finished product will hinge on the selection and level of active ingredients and excipients, the aesthetics and even the penetration of these actives into the stratum corneum will be affected by the product rheology. Rheology modifiers are frequently denoted as thickeners and, whilst increasing the apparent viscosity should enhance the perception of quality in a formulation, this is only one aspect of rheological control. The product itself can be Newtonian or pseudoplastic, thixotropic, exist as a ringing gel or a stringy flowable liquid. This changes the way that the product appears in the bottle, the ease with which aliquots are poured or scooped from the packaging, the process of rubbing it into the skin or along the hair shaft, and upon using, the rinsing and removal of the product. It will also be vital to select the correct rheological characteristics to guarantee the stability of the finished formulation. By changing the structure of polymeric rheology modifiers, the impact on the sensorial properties and performance characteristics can be investigated. Careful selection of monomers, structure and other co-ingredients will result in products optimised for use in skin care formulations.
Perspectives on the Development of the Personal Care Industry
Authors: Loh Xian Jun
Published: July 2016

This chapter aims to present an overview of the trends for personal care and to identify the challenges, drivers and restraints. Through this analysis, I will identify and discuss areas that could represent potential targets for growth and provide recommendations and conclusions for people involved in this industry to evaluate business growth opportunities.
Synthesis and structure of ruthenium-fullerides
Authors: Leng F. , Gerber I. C. , Lecante P. , Bacsa W. , Miller J. , Gallagher J. R. , Moldovan S. , Girleanu M. , Axet M. R. , Serp P.
Published: July 2016

We report a simple and original procedure for preparing Ru–C60 polymeric chains, which spontaneously self-assemble as polymeric spherical particles, and can be surface decorated with Ru nanoparticles.
Hierarchical polypyrrole/Ni3S2@MoS2 core–shell nanostructures on a nickel foam for high-performance supercapacitors
Authors: Gao Jie , Wang Xiuhua , Wang Xiuqin , Que Ronghui , Fang Yao , Shi Bo , Wang Zhenghua
Published: July 2016

Hierarchical polypyrrole/Ni3S2@MoS2 core–shell nanostructures have been successfully designed and constructed on a Ni foam substrate through a facile two-step solution synthesis protocol and exhibit high performance as a supercapacitor.
Improving crystallization and processability of PBS via slight cross-linking
Authors: Liu Gui-Cheng , Zhang Wen-Qiang , Zhou Shui-Lian , Wang Xiu-Li , Wang Yu-Zhong
Published: July 2016

PBS containing a cross-linkable comonomer containing an alkynyl group can slightly cross-link during the preparation, which makes PBS show a fast crystallization rate and high melt viscosity.
High luminance of CuInS2-based yellow quantum dot light emitting diodes fabricated by all-solution processing
Authors: Li Jingling , Jin Hu , Wang Kelai , Xie Dehui , Xu Dehua , Xu Xueqing , Xu Gang
Published: July 2016

In this work, all-solution processed, multi-layer yellow QLEDs, consisting of a hole transport layer of poly(9-vinylcarbazole), emissive layer of ligand exchanged CuInS2/ZnS QDs, and electron transport layer of ZnO nanoparticles, are fabricated.
Activation of PPARβ/δ prevents hyperglycaemia-induced impairment of Kv7 channels and cAMP-mediated relaxation in rat coronary arteries
Authors: Morales-Cano Daniel , Moreno Laura , Barreira Bianca , Briones Ana M. , Pandolfi Rachele , Moral-Sanz Javier , Callejo Maria , Mondejar-Parreño Gema , Cortijo Julio , Salaices Mercedes , Duarte Juan , Perez-Vizcaino Francisco , Cogolludo Angel
Published: July 2016

PPARβ/δ activation protects against endothelial dysfunction in diabetic models. Elevated glucose is known to impair cAMP-induced relaxation and Kv channel function in coronary arteries (CA). Herein, we aimed to analyse the possible protective effects of the PPARβ/δ agonist GW0742 on the hyperglycaemic-induced impairment of cAMP-induced relaxation and Kv channel function in rat CA. As compared with low glucose (LG), incubation under high glucose (HG) conditions attenuated the relaxation induced by the adenylate cyclase activator forskolin in CA and this was prevented by GW0742. The protective effect of GW0742 was supressed by a PPARβ/δ antagonist. In myocytes isolated from CA under LG, forskolin enhanced Kv currents and induced hyperpolarization. In contrast, when CA were incubated with HG, Kv currents were diminished and the electrophysiological effects of forskolin were abolished. These deleterious effects were prevented by GW0742. The protective effects of GW0742 on forskolin-induced relaxation and Kv channel function were confirmed in CA from type-1 diabetic rats. In addition, the differences in the relaxation induced by forskolin in CA incubated under LG, HG or HG + GW0742 were abolished by the Kv7 channel inhibitor XE991. Accordingly, GW0742 prevented the down-regulation of Kv7 channels induced by HG. Finally, the preventive effect of GW0742 on oxidative stress and cAMP-induced relaxation were overcome by the pyruvate dehydrogenase kinase 4 (PDK4) inhibitor dichloroacetate (DCA). Our results reveal that the PPARβ/δ agonist GW0742 prevents the impairment of the cAMP-mediated relaxation in CA under HG. This protective effect was associated with induction of PDK4, attenuation of oxidative stress and preservation of Kv7 channel function.