bluuebunny/crossref_metadata_2025_split huggingface dataset:
Applications of methods of operations research and modern economic theory
Authors: van Klinken J. 
Published: July 2016

It is rather a pity that we received only three papers especially devoted to subject 2, “applications of methods of operations research and modern economic theory”. Maybe the time for real applications of operations research techniques in the insurance field has still to come. However, I am convinced that sooner or later such techniques—in connection with the use of the computor—will play a more or less important part in the management of insurance business. An impulse to this of course will be the appearance of —let me say—“textbooks” on this subject; such as the book written by Wolff, Methoden der Unternehmensforschung im Versicherungswesen, Springerverlag 1966, a copy of which I received a few days ago.Meanwhile, the fact that only a few papers have been sent in gives me the opportunity to report on them in some detail and to make a few side remarks.The studies presented are:Borch. Dynamic decision problems in an insurance company, de Leve and Weeda. Driving with Markov-programming.d'Hooge, Franckx and Gennart. Utilisation pratique de la méthode de simulation dans l'assurance “non-life”.The paper Prof. Borch submitted, deals essentially with some problems related with random walk theory. Partly it can be considered to be the counterpart of the classical discontinuous ruin theory as its subject is the expected duration of life of the company and maximisation of the discounted value of dividend payments.The question of calculating the expected duration of life and more specially the means the company has to influence its future lifetime involves reinsurance and utility theory to which topic in recent years Prof. Borch has devoted a number of very interesting publications.
Calcul des Primes et Marchandage
Authors: Briegleb Danielle , Lemaire Jean 
Published: July 2016

Two premium calculation principles by negotiation. Using, as main tools,the classical risk exchange model by Borch andthe bargaining models of Nash and Kalai-Smorodinsky,we define two new premium calculation principles, whose main goal is to take explicitly into account the attitude towards risk of the policy-holders. Those principles are neither additive nor iterative, but they nevertheless possess several important properties: the premium is translation-invariant, it does not depend neither on the reserves nor on the portfolio of the company; it takes into account all the moments of the claim distribution; it is independent of the policy-holder's wealth but increases with his risk aversion.Coalition against an insurance company. While computing the core of this risk exchange, we show that it can be of the policy-holder's interest to coalize in order to obtain premium cuts.Le modèle d'échange de risques de Borch entre plusieurs compagnies d'assurances soucieuses d'améliorer leur situation en formant un pool de réassurance a fait l'objet de très nombreuses publications. Ce n'est que depuis quelques années cependant que l'on semble s'être aperçu que le même modèle pouvait être utilisé pour décrire toute économie d'échange, en particulier le contrat d'assurance simple entre un assuré et sa compagnie. Si l'on suppose que les préférences de l'assuré peuvent être décrites par une fonction d'utilité exponentielle, et que l'assureur est indifférent au risque en première approximation, les contrats Pareto-optimaux consistent en une couverture complète du risque, moyennant le paiement d'une prime que le critère de Pareto-optimalité ne permet pas de déterminer.
Premium Calculation for Deductible Policies with an Aggregate Limit
Authors: Mack Thomas 
Published: July 2016

AbstractIn Industrial Fire insurance an aggregate limit for the amount retained by the policyholder under a deductible policy has been agreed upon more frequently in recent times. This agreement is equivalent to a stop-loss cover on the retained loss amount. For the Poisson-lognormal model the corresponding stop-loss net premium is calculated using various methods (normal power, translated gamma, various discretisations) and the methods are compared. Finally, the influence of the model parameters is examined and it is demonstrated how a variety of parameter value combinations can be reduced to only a few rating curves.
Approximating the Distribution of a Dynamic Risk Portfolio
Authors: Jewell William S. 
Published: July 2016

AbstractIn a previous paper, Jewell and Sundt showed how to approximate a distribution of total losses from a large, fixed, heterogeneous portfolio, using a recursive algorithm developed by Panjer for the distribution of a random sum of random variables (a single casualty contract). This paper extends the approximation procedure to large, dynamic heterogeneous portfolios, in order to model either a portfolio of correlated casualty contracts, or a future portfolio, whose composition is not known with certainty.
The propensity to cause accidents
Authors: von Lanzenauer Christoph Haehling , Lundberg William N. 
Published: July 2016

Information relating to the expected number of losses is of importance in automobile insurance systems. The distribution of risks by number of losses per year may be based on the following model
with λ representing the average number of losses per year. This distribution is the Poisson distribution. Tests of this model versus actual observations often indicate significant deviation. This discrepency can result from the constancy of λ which makes the model appropriate for an individual but would require an isohazardous population when applied to a group of individuals. In reality, however, λ will vary from individual to individual. A model accounting for this spread in λ is given in
where z(λ) is a distribution describing the spread of λ. The results of model (2) certainly will depend on the form of z(λ). It has been hypothesized that z(λ) can be represented by (3)
which is a Pearson Type III [1, 5, 7]. With this assumption model (2) becomes the negative binominal distribution

with a mean of

and a variance of
If the observed mean is and the observed variance it is possible to determine a and b by solving the above equations for mean and variance. Thus

and
The results indicate an improved fit to actual observations [1, 5, 6].
Tariffing of Consequential Loss Insurance
Authors: Johansen Paul 
Published: July 2016

In the following, consequential losses after fires are considered. A generalisation to consequential losses after other risks is most likely rather trivial.The purpose of this paper is rather asking questions and putting a problem before the readers than presenting solutions. According to our experience, little has been done to seek logical systems or to construct mathematical or physical models in order to study these problems. The volume of business is rapidly growing but it could grow much more if a more reasonable tariffing was made. Many insured with fire insurances hesitate to take out an additional consequential coverage. They can see the need of the coverage, but they will not accept—and rightly—the present market rates. Actuarial colleagues are invited to join in building up suitable models to guide the practical underwriter.The office premium today is most often composed of the following parameters:a. the premium rate of the corresponding fire insuranceb. the insurance sum, defined e.g. as the expected turnover less variable costsc. the coverage period, an upper limit of the period in which indemnity can be given. In Denmark, for a period of 12 months the premium of a consequential loss' insurance is normally defined as the insurance sum multiplied by the fire premium + 25 per cent.We shall regard various risk situations in order to study the relationship between the fire risk and the consequential loss. The most simple situation is an undertaking where practically spoken only total fire losses will occur. One may think of a fireworks factory or a telephone exchange building. The fireworks factory will burn out physically. After a fire the contents of the telephone building, even if the majority of the materials is at hand, will be worthless because of the corrosion caused by the PVC contents of the wires. In the cases mentioned, an outbreaking fire might, of course, be extinguished so early that practically no damage will occur. If the fire, however, exceeds a certain extent, a total loss is likely to follow.
Notes sur la distribution conditionnée du montant d'un sinistre par rapport à l'hypothèse qu'il y a eu un sinistre dans l'assurance automobile
Authors: Benktander Gunnar 
Published: July 2016

Dans un traité antérieur, l'auteur a examiné, en collaboration avec M. Segerdahl, un certain nombre de fonctions analytiques propres à définir la distribution du montant d'un sinistre en s'arrêtant tout spécialement aux aspects présentant de l'intérêt du point de vue de l'assurance en excédent de sinistres. L'examen a révélé que les répartitions du type Pareto étaient intéressantes aussi bien du point de vue théorique — en tant que représentant un type de distribution particulièrement „dangereux” — que du point de vue pratique, le matériel statistique suédois et norvégien obtenu lors de l'analyse de différentes branches d'assurances — telles que Vie, Incendie et Automobile — semblant bien indiquer que pour de grands intervalles la distribution du type Pareto représenterait l'authentique matériel des dommages.Nous nous permettrons par conséquent de nous arrêter tant soit peu aux caractéristiques de la distribution du type Pareto ainsi qu'aux formules découlant de la dite distribution pour la prime de risque en excédent de sinistres et ses variances.Si P(x) exprime la distribution, I − P(x) = H(x) = C. x−∝ pour a < x ≤ M, M étant la valeur la plus grande pour x, en supposant que la probabilité d'atteindre la valeur M est H(M) = C. M−∝.Si m(x) est la moyenne des portions de sinistres supérieures à xSpécialement si M = ∞ on obtient .
Sur L'efficacité des critères de tarification de l'assurance contre les accidents d'automobiles
Authors: Delaporte Pierre 
Published: July 2016

Les accidents d'automobiles surviennent lorsqu'il se produit un ensemble de circonstances défavorables plus ou moins fortuites. Ces circonstances sont liées au véhicule, à son conducteur, à l'usage qui en est fait, à la région dans laquelle il circule et à beaucoup d'autres faits souvent difficiles à caractériser.L'assureur ne peut évidemment connaître qu'une faible partie de ces caractéristiques, c'est pourquoi il considère la survenance de l'accident comme un fait aléatoire. Cependant, les dépouillements statistiques des nombres d'accidents arrivés à des véhicules ayant un même ensemble de caractéristiques montrent que la fréquence moyenne, c'est-à-dire le nombre d'accidents survenus divisé par le nombre de voitures-année, varie avec cet ensemble de caractéristiques communes qui constitue alors une classe du tarif d'assurance. La détermination du montant de la prime à demander pour garantir le véhicule est alors faite par l'assureur en demandant une prime hiérarchisée selon la fréquence moyenne et selon le coût moyen des sinistres de la classe du tarif.Si l'on ajoutait de nouveaux critères de tarification à ceux déjà utilisés, il est évident qu'on trouverait une diversification plus grande des primes; ceci montre donc qu'à l'intérieur d'une classe de tarif tous les risques des véhicules ne sont pas égaux.Dans la présente étude, nous rechercherons d'abord quelle part de l'hétérogénéité des risques des voitures est utilisée par les diverses caractéristiques figurant dans le tarif français d'assurance de la responsabilité civile des propriétaries de véhicule. Nous rechercherons alors s'il existe une limite à la précision du tarif.
On the Numerical Calculation of the Distribution Functions Defining Some Compound Poisson Processes
Authors: Philipson Carl 
Published: July 2016

1. The comfound Poisson process in the wide sense is defined as a process for which the probability distribution of the number i of changes in the random function attached to the process, while the parameter passes from o to a fixed value τ of the parameter measured on a suitable scale, is given by the Laplace-Stieltjes integral
where U(ν, τ) for a fixed value of τ defines the distribution of ν. U(ν, τ) is called the risk distribution and is either τ-independent or, dependent on ν, τ.2. The compound Poisson process in the narrow sense is defined as a process for which the probability distribution of the number of changes can be written in the form of (I) with a τ-independent risk distribution.In their general form these processes have been analyzed by Ove Lundberg (1940). For such processes the following relation holds for the probability of i changes in the interval ο to τ, P̅i (τ) say
this relation does not hold for processes with τ-dependent risk distribution. Hofmann (1955) has introduced a sub-set of the processes concerned in this section for which the probability for non-occurrence of a change in the interval o to τ is defined as a solution of the differential equation
and ϰ ≥ o; the solutions may be written in the form where η is independent of and of two alternative forms one for ϰ = I and one for other values of ϰ. The probabilities for i changes in the interval o to τ in the processes defined by the solutions of Hofmann's equation are derived by Leibniz's formula, and are designated by and, in this paper, called Hofmann probabilities.
Analytical steps towards a numerical calculation of the ruin probability for a finite period when the riskprocess is of the Poisson type or of the more general type studied by Sparre Andersen
Authors: Thorin Olof 
Published: July 2016

As is well-known, in the early 60's a Swedish committee set to work at the numerical calculation of the distribution function of the total amount of claims and of the related stop loss premiums in the Poisson and Polya cases (Bohman and Esscher [6]). Since the characteristic function for the said distribution function was easily available in terms of the characteristic function for the distribution function of an individual claim, the committee chose to base the numerical calculations on the C-method by H. Bohman (Bohman [5]). The calculation of the ruin probability for a finite or infinite period was not considered by the committee.The last-mentioned problem has now been taken up by a new committee formed by the Swedish Council for Actuarial Science and Insurance Statistics. The committee—consisting of H. Bohman, J. Jung, N. Wikstad and the present author—has to consider several aspects of the practical applicability of the collective risk theory. However, without possibilities of calculating—at least approximately—the ruin probability for a finite period the applicability of the existing ruin theories seems to be rather limited, so the committee has looked around for such possibilities. At the present stage the committee is considering the classical Poisson theory and Sparre Andersen's generalization of this theory [2]. It is the hope of the committee that, at a later stage, also the Polya theory and the theory recently presented by Segerdahl [11] combining the Sparre Andersen theory and the Polya theory may be treated.
Distribution Free Approximations in Applied Risk Theory
Authors: Andreasson Gunnar 
Published: July 2016

Most large insurance companies have today electronic computers that enable not only efficient actuarial statistics, but also research in applied risk theory. An important task in this latter field is the developing of an information system for control of the business as to the statistical balance between premiums and claims. The entire system can be separated into two parts, one descriptive and one analytic part. The descriptive part, that also may be called statistics production, is the base of the whole system and must be constructed in a general way to make it possible to apply mathematical tools in risk analysis. For the analytic part and its applications for computers there is a growing interest among actuaries as can be noticed from the reports in actuarial journals. The classical models of collective risk theory have recently been extensively illustrated by numerical calculations performed by the convolution committee in Sweden.When starting to construct the analytical part of the information system one finds that in spite of programming for the computer there is firstly a hard work to find realistic mathematical models, especially mathematical expressions for claim distributions, and secondly to estimate their parameters. According to the mathematical theory of risk, or the risk process, it is necessary to assume and test specific mathematical forms of two distributions, the number of claims and claims amount.
The recent Development of Risk Theory and its Applications
Authors: Kupper J. 
Published: July 2016

The response to the invitation for the 5th Colloquium has been, especially for subject 1, very gratifying; a large number of meritorious papers have been sent in. Fortunately, it took not much time in this case to find a good guide for all this work. R. E. Beard presents in his article “Some Actuarial Aspects of Non-Life Insurance Company Management”) a broad cross-section of the many problems that confront the non-life insurer. It was therefore regarded as not quite unwise to follow his steps and to discuss the other papers at suitable points.In the first half of his work R. E. Beard deals with a practical example from motor insurance, which is fully calculated with the help of numerical data. The question relates to the estimation of the value of outstanding claims, a quantity which is of decisive importance for the evaluation of the results of a portfolio. Apart from chance fluctuations which might affect the statistics from year to year, there are three major factors that render the task of estimation difficult:(a) the natural growth of the portfolio(b) the fact that bigger claims require longer time for settlement than the smaller ones(c) the change in the value of money with time.
On Risk Processes with Stochastic Intensity function
Authors: Grandell Jan 
Published: July 2016

In this paper we are going to study some properties of a stochastic process, which has been proposed by Cramér (1968) as a model of the claims arising in an insurance company. This process has been studied by Cox in a different context. A few elementary results, concerning moments, are given by Cox and Lewis (1966). The present paper will be a survey of some results derived by the author (1970:1) and (1970:2). For detailed proofs we refer to these papers.Let λ(t) be a real-valued stochastic process, such that P{λ(t) < o} = o. We further assume that Eλ(t) = 1 and that Eλ2(t) < ∞ for every fixed value of t. We denote the covarianceThe process λ(t) will play the role of an intensity function. That means, that for every fixed realization of the process, the probability ofand that the number of events in disjoint intervals are independent.We now define a point process N(t), where N(t) is the number of events which have occurred in (o, t]). With this definition we getwhereThe integral is assumed to exist almost surely. This process will be called the N-process.
A note on some compound poisson distributions
Authors: Philipson Carl 
Published: July 2016

At the Lundberg Symposium, Stockholm 1968 Jung and Lundberg presented a report on similar problems as those treated in this note, and to the Astin colloquium, Berlin 1968 the present author presented a report with the same title as this note, where some of the results in the first-mentioned report were commented upon. Jung and Lundberg kindly discussed the topic here concerned with the present author some time after the colloquium. On account of this discussion, the present author withdrew his report from the publication in its original form. The following context is a revision and a completion of the author's report to the colloquium.Let τ be a parameter measured on its original, absolute scale, and let be the same parameter measured on an operational scale with respect to the probability distribution (or the corresponding for t). The parameter will often be referred to as “time”, which does not imply a restriction of the theory to proper time parameters.A random function X(s) is said to be distributed in a cPd i.w.s. (compound Poisson distribution in the wide sense), if the distribution function of X(s) for every fixed parameter point (s, τ) in a finite or infinite domaine of the parametric space as a function of τ can be written in the following general formwhere the asterisk power m*, here and throughout this note, is taken to mean, for m ˃ O, the m times iterated convolution of the distribution function with itself, and, for m = o, unity. W(x, s) being the conditional distribution function of the size of one change in X(s) relative to the hypothesis that the change has occurred at s, here abbreviated to the change distribution. U(ν, τ) is a distribution function, called the structure function. In the general case V(x, s) and U(ν, τ) may depend on s and τ respectively. If, particularly, these functions are supposed to be independent of the parameter, they will be denoted V(x), U(ν) respectively. In the particular case, where V(x) = ε(ν—c1), c1 being an arbitrary but fixed constant and ε(ξ), here, and in the following context, the unity distribution equal to zero for negative values, and to unity for non-negative values of ξ, the cPd is said to be elementary and, in the opposite case, non-elementary. In the elementary case the distribution of X(s) is defined by the integral appearing in (Ia) with x = c1, so that W(x, s) = W(x) = I.
On The Estimation of Means and Variances In The Case Of Unequal Components
Authors: Hovinen Esa 
Published: July 2016

In practical statistical work one frequently meets certain problems. For instance, we may have the following data about loss ratios in certain insurance companies and corresponding, numbers of insurance in force:I assume further that we have no reason to believe that the companies, their loss ratios and their structure of insurances in force differ in any other way than by the size of companies. The problem is how to get quick estimates of mean losses and their variances in different companies?A straitforward way to estimate the mean loss ratio would be to compute the usual mean of numbers pi, (Σpi/6) = 14; its standard deviation is 6,5. As this procedure of the “first statistician” seems to be too simple and naive, a “more cautious” statistician would compute the weighted mean loss ratioThe “more cautious” statistician would arque that his result is much better than the other result 14. But what would be the variance of the estimate 7,1, and what is the variance in the different companies?