bluuebunny/crossref_metadata_2025_split huggingface dataset:
Driving with markov-programming
Authors: de Leve G. , Weeda P. J. 
Published: July 2016

Let us consider the following problem.A motorist has decided to effect an accident insurance under the following conditions. The insurance runs for one year. The premium for the first year amounts E0. If no damages have been claimed during i successive years, i = 1, 2 or 3 the premium is reduced to Ei. After four years of damagefree driving no further premium reduction is granted, so the premium remains E3. The premium is due on the first day of the year. The own risk amounts a0.The number of accidents of our motorist during a time period T is assumed to be Poisson distributed with parameter λT. The extent of the damage has distribution function F(s) with finite mean and variance.The problem of our motorist will be to decide whether to claim a damage or not. He will have to develop a strategy that specifies his decisions in every possible situation. His strategy will be called optimal if it minimizes the expected costs in the long run.We may expect that in view of the premium reduction, it will be unprofitable to claim damages which are not much larger than a0. Once a damage is claimed it will be profitable to claim all following damages that exceed a0 during the remaining part of the year.Hence his decisions will also depend on the time of the year and the premium paid at the beginning of that year. So we distinguish between four types of years, for each premium one.
Large Claims in Insurance Mathematics
Authors: Teugels Jef L. 
Published: July 2016

I take great pleasure in addressing this audience. As you might know I'm a mathematician with a deep interest in insurance mathematics. As such, it is my sincere opinion that the gap between practising actuaries and theoretical researchers can be made substantially smaller. If my contribution can help in bridging the gap, I will feel fully compensated for the effort it took to prepare this lecture and the results contained therein.The simple fact that we meet on the occasion of the sixteenth ASTIN Colloquium gives me a challenging opportunity to help in creating a platform on which both theoreticians and practitioners can meet.The subject of my lecture stems from a long interest in large claims: What are they? Are they really dangerous? Is there a way to get them under control? Can one recognize them in practical situations?I like to express in simple mathematical terms some results that might help in acquiring better insight on the impact of large claims in insurance mathematics. Perhaps, no result will be of immediate applicability as reality is too complicated to be described by the simplicity of the results to follow. Nevertheless the latter can be considered as building blocks of a real world in which one has to tackle large claims in theory as well as in practice.
A Stable Recursive Algorithm for Evaluation of Ultimate Ruin Probabilities
Authors: Goovaerts Marc , de Vylder Florian 
Published: July 2016

AbstractProbabilities of ruin are solutions of differential or integrodifferential equations. Solving such equations numerically can be performed by means of approximate quadrature formulae for the convolution part of the equation. In this contribution it is shown how applicable recursion formulae, giving results within a prescribed tolerance level, can be obtained. Some numerical results are displayed.
Homogeneous Premium Calculation Principles
Authors: Reich Axel 
Published: July 2016

AbstractA premium calculation principle π is called positively homogeneous if π(cX) = cπ(X) for all c > 0 and all random variables X. For all known principles it is shown that this condition is fulfilled if it is satisfied for two specific values of c only, say c = 2 and c = 3, and for only all two point random variables X. In the case of the Esscher principle one value of c suffices. In short this means that local homogeneity implies global homogeneity. From this it follows that in the case of the zero utility principle or Swiss premium calculation principle, the underlying utility function is of a very specific type.A very general theorem on premium calculation principles which satisfy a weak continuity condition, is added. Among others the proof uses Kroneckers Theorem on Diophantine Approximations.
Rate Making and Society's Sense of Fairness
Authors: de Wit G. W. , van Eeghen J. 
Published: July 2016

Actuaries have always been in search of ways to determine premiums which match the risks insured as closely as possible. They do this by differentiating between them on the basis of observable risk factors. In practice, many examples of such risk factors are being used: age and sex for life insurance; location, type of building etc. for fire insurance. Motor insurance is perhaps the most characteristic branch with respect to this phenomenon: in tariffs we find factors like weight, price or cylinder capacity of the car, age of the driver, area of residence, past claims experience (Bonus/Malus), annual mileage etc.Outsiders may not always be very positive about such a refined premium differentiation. The basis of insurance, they say, should be solidarity among insureds; premium differentiation is basically opposed to this. Another statement heard in the field is: “Premium differentiation ultimately results in letting every individual pay his own claims, it is the end of insurance”.Much confusion arises during discussions about this subject, especially between actuaries and non-actuaries. We will therefore first give a mathematical definition of solidarity, (Section 2), followed by a brief description of certain trends in society which might bring insurers to deliberately drop certain risk factors from their tariffs in order to increase solidarity (Section 3). The consequences of doing so are examined and it is shown that increased solvency requirements will in the end prove to be ineffective. A possible solution is a voluntary transfer of premium between companies (Section 4). The situation is illustrated by an example of health insurance in the Netherlands, where proposals to arrive at such transfeis are presently being discussed.
Optimal Risk Exchanges
Authors: Bühlmann Hans , Jewell William S. 
Published: July 2016

The determination of optimal rules for sharing risks and constructing reinsurance treaties has important practical and theoretical interest. Medolaghi, de Finetti, and Ottaviani developed the first linear reciprocal reinsurance treaties based upon minimizing individual and aggregate variance of risk. Borch then used the economic concept of utility to justify choosing Pareto-optimal forms of risk exchange; in many cases, this leads to familiar linear quota-sharing of total pooled losses, or to stop-loss arrangements. However, this approach does not give a unique, risk-sharing agreement, and may lead to substantial fixed side payments. Gerber showed how to constrain a Pareto-optimal risk exchange to avoid invasion of reserves.To these ideas, the authors have added the actuarial concept of long-run fairness to each participant in the risk exchange; the result is a unique, Pareto-optimal risk pool, with “quota-sharing-by-layers” of the total losses. There are many interesting special cases, especially when all individual utility functions are of exponential form, giving linear quota-sharing-by-layers. Algorithms and numerical examples are given.
The Credible Distribution
Authors: Jewell William S. 
Published: July 2016

AbstractCredibility theory is concerned with the problem of forecasting the mean performance (claim frequency, total losses, etc.) of an individual risk, selected from a collective of heterogeneous risks, based upon the statistics of the collective, and upon the individual's experience data. The classic results, derived by American actuaries in the 1920's, were further strengthened by Bailey and Mayerson in 1950 and 1965, who showed that these results were exact Bayesian for certain risk distributions. Bühlmann, in 1967, then showed that the credibility formulae were the best least-squares linearized approximation to the exact Bayesian forecast, for general risk distributions.This paper extends credibility theory to the problem of forecasting thedistributionof individual risk, based upon collective statistics and individual experience data. Although the problem is, in principle, solved by finding a Bayesian conditional distribution, this approach requires a detailed knowledge of collective structure. Thecredible distribution, on the other hand, requires fewer prior statistics, and is also a best least-squares linearized approximation to the exact Bayesian distribution.Following the theoretical development, detailed computational results are given.
Experience Rating with Credibility Adjustment of the Manual Premium
Authors: Taylor G. C. 
Published: July 2016

AbstractA common procedure for experience rating is to use Whitney's credibility formula with the manual premium per risk unit estimated by the observed average claim amount per risk unit. As pointed out by Whitney himself, this observed average also needs to be subjected to credibility adjustment. This suggestion is pursued in the paper and an experience rating procedure developed in which there are two stages:(i) revision of the prior expected manual premium in accordance with the observed average claim amount per risk unit;(ii) experience rating of the individual risk classes by the usual methods but using the manual premium obtained in stage (i).Both stages of this procedure involve credibility indices, for which formulae are developed.Conditions under which the “common procedure” referred to above is fairly reliable are found and it is seen, somewhat surprisingly, that the procedure is often more valid than one expects on intuitive grounds. Care is necessary, however, when there are wide differences in size between different risk classes.
Economic Factors in Liability and Property Insurance Claims Costs
Authors: Masterson Norton E. 
Published: July 2016

The original paper with this title was published in 1968, following presentation at a Casualty Actuarial Society meeting. This is another up-date of indexes in the economic model—first report of 1976 and a forecast for 1977. These LPI indexes measure economic factors affecting loss and loss adjustment settlement costs which are incurred after claims have been reported. The indexes measure direct claims costs and not the reinsured excess losses which would be more adversely affected by inflation.This is a Claims Market Place concept of the loss settlement function of the insurance company. Claims Costs (our economic cost of production) result from purchasing of services under unusual circumstances in controversial, severe, hasty and often emergency situations. Claims settlements can take place in court rooms, lawyers' offices, repair garages and hospitals. The legalistic atmosphere is often one of friction and excessive demand rather than of a normal commercial esprit de corps. The procurement of these claims services requires dealing with high cost furnishers of services: doctors, clinics, hospitals, lawyers, repair garages or body shops, building trades, house furnishings.
Earthquake Insurance in Japan
Authors: Wakuri Masao , Yasuhara Yasuyuki 
Published: July 2016

Japan is one of the most earthquake-prone countries in the world and a considerable volume of earthquake insurance is written by private insurers. Therefore, a report on earthquake insurance in Japan has been prepared for the 13th ASTIN Colloquium.We will first summarise, from recent results of seismological studies, the matters which would form the basis for a study of earthquake insurance, and then explain how this insurance actually works in Japan.
Survival Probabilities Based on Pareto Claim Distributions
Authors: Seal Hilary L. 
Published: July 2016

It is commonly thought that the characteristic function (Fourier transform) of the Pareto distribution has no known functional form (e.g. Seal, 1978, pp. 14, 40, 57). This is quite untrue. Nevertheless the characteristic function of the Pareto density is conspicuously absent from standard reference works even when the Pareto distribution itself receives substantial comment (e.g. Haight, 1961; Johnson and Kotz, 1970, Ch. 19; Patel, Kapadia and Owen, 1976, § 1. 5).The Pareto density may be writtenwith distribution functionmean = p/(v − 1) and variance = b2v(v − 1)2(v−2). These are infinite when v≤1 and v≤2, respectively. Its Laplace transform (s= c + iu)where E is the generalized exponential integral (Pagurova, 1961) and can be written in terms of incomplete gamma or confluent hypergeometric functions (Slater, 1960, Sec. 5.6). When s = − it β(s) becomes the characteristic function (see Appendix I).As Benktander (1970) tells us, the Pareto distribution has been particularly successful at representing the distribution of the larger claim amounts. In earlier years it was employed to represent the distribution of life insurance sums assured but more recently it has been used for the claim distributions of fire and automobile insurance. Table 1 provides the v-values we have been able to locate. Note that the variance of the distribution is infinite when v≤2 and if it were not for the anomalous v-values of Andersson (1971) we would have ventured the opinion that modern claim data encourage the assumption that v>2. In our numerical work we have used v = 2.7 and smaller values might change some of the computer rules we have proposed in Appendix II.
Evaluation of the Capacity of Risk Carriers by Means of Stochastic-Dynamic Programming
Authors: Pentikäinen T. , Rantala J. 
Published: July 2016

The Ministry of Social Affairs and Health, being the Supervising Office of Insurance in Finland, has established a special working group to investigate the problems involved with the solvency of insurers. A report will be compiled in a near future. The capacity of risk carriers is one of the problems dealt with, and it will be preliminarily reviewed in this paper.The problem was treated by the working group parallelly by means of1. an empirical approach observing actual fluctuations in underwriting gains of insurers, and2. a theoretical approach, constructing a stochastic-dynamic model and studying its behaviour, especially its sensitivity to numerous background factors.First the methods of investigation are described and their application is then demonstrated using some numerical data. Because a comprehensive report will be published by the working group separately, only the main schedule is given. For the same reason the consideration is limited here to stochastic risks, omitting the fact that the solvency of an insurer is also jeopardized by numerous “non-stochastic” risks such as failure in investments, political interference of the authorities, mismanagement of the company, or misappropriation of its property.
The Bargaining Set of a Reinsurance Market
Authors: Baton Bernard , Lemaire Jean 
Published: July 2016

This paper uses the same notations and some of the results of Baton and Lemaire (1981). The reader is referred to that work for more details about the classical risk exchange model, which will not be recalled here. The main result of that former paper was to characterize the core of the market in the case of exponential utilities, and to show that it is never empty. Since the core always exists, and since it is such an intuitive notion, one might wonder why we introduce here a much more complicated concept. The reason is that the core is presently subject to a heavy fire of criticisms–both experimental and theoretical–from leading researchers in game theory; they claim that the core is much too static, that it does not take into account the real dynamics of the bargaining process, that it does not introduce the full spectrum of negotiation threats of the traders. Indeed, experimental data consistently produce final payoffs that lie outside the core, but within the bargaining set (abbreviated: b.s.). We shall attempt to illustrate those criticisms in 4. We shall define the b.s. in a general non transferable game in 2, and characterize it in the special case of a 3-company reinsurance market in 3, but first of all we would like to explain intuitively the basic mechanisms of the b.s. by means of a simple example (with transferable utilities).The basic difficulty in modelling a negotiation process is to express what is the purpose of the game. Certainly, the objective is not just to get the maximal amount of profits, because if everyone demands the highest payoff he can obtain in a coalition, no agreement will be reached; the goal of the process is to attain some state of stability, to which the bargainers should agree if they want any agreement to be enforced. This stability should reflect in some way the power of each player, which results from the rules of the game, his initial situation, his attitude towards risk, …A bargaining process is a multi-criteria situation, in which the players certainly attempt to maximize their payoffs, but also try to enter into a “safe” or “stable” coalition.
Novelties in Swedish Automobile Insurance Rating
Authors: Lanteli Gunnar 
Published: July 2016

On March 10th, 1961, the majority of the Swedish Automobile Insurance Companies introduced a remarkable novelty in automobile insurance rating, a rating plan for private passenger cars partly based on a recent statistical investigation of the variation of risk with some characteristics of the driver and the vehicle. These characteristics had not until then been used for classification purposes, nor had they been studied in our current experience.For a long time the Swedish rating plan has classified private passenger cars by geographical district (3), merit class or „bonus class” (7) and (for Auto Physical Damage only) horsepowers (8). Teetotallers enjoy a special discount of 20%.In spite of this rather far-going subdivision, founded on an elaborate statistical experience it was quite obvious that some important element was missing, as different companies operating in the same market showed significantly deviating underwriting experience. The tariff association „Svenska Bilförsäkringsföreningen” (SBF) and some other independent companies agreed to make a special investigation to find the cause of this adversity. A small committee was appointed to handle the question. From the start it was clear that some kind of inquiry had to be made among the policy holders of the participating companies. The information we needed was if and how different attributes such as sex, age, marital status, occupation, use of the car, annual mileage etc. influenced the risk. To inquire all of our private passenger carowners would have been too costly so we had to choose between a random sample and some other kind of limitation.
Quelques réflexions sur la réforme du tarif français d'assurance automobile
Authors: Thepaut Andre 
Published: July 2016

Très nombreux sont les assureurs français qui paraissent admettre aujourd'hui la nécessité de réformer les méthodes actuelles de tarification de l'assurance automobile. De nos jours en effet la possession d'un véhicule automobile n'est plus le privilége de la classe bourgeoise aisée; de très nombreux petits fonctionnaires, employés, artisans et ouvriers tant à la ville qu'à la campagne considèrent un tel véhicule comme absolument indispensable à la vie moderne. Cet état d'esprit est particulièrement vrai chez les jeunes ménages pour lesquels le véhicule automobile se situe tout à fait au sommet de la hiérarchie des besoins, immédiatement après la chambre à coucher et bien souvent avant la salle de bains ou le frigidaire.Pour mesurer l'ampleur du problème ainsi posé aux assureurs, il est utile d'examiner le tableau de l'annexe n° 1 extrait d'une étude récente faite par l'I.N.S.E.E. à la demande du centre de recherches et de documentation sur la consommation (C.R.E.D.O.C.) et publiée en Décembre 1960.On constate notamment que:1°/ sur 4.539.000 véhicules à 4 roues, 1.053.000 appartiennent à des ouvriers ou à du personnel de Service et 657.000 à des agriculteurs;2°/ ces véhicules sont achetés d'occasion pour la plupart;3°/ leur kilométrage annuel est très inférieur au kilométrage moyen général; autrement dit la dispersion des kilométrages autrefois relativement faible parait s'être accrue très considérablement ces dernières années.Ces constatations expérimentales s'expliquent d'ailleurs aisément si l'on songe aux ressources limitées dont disposent ces “marginaux” de l'automile qui, d'ailleurs, ont bien souvent acheté leur vehicule à crédit.
Problems in Motor Insurance — Claim Reserves
Authors: Masterson Norton E. 
Published: July 2016

In his comprehensive paper entitled “A General Survey of Problems Involved in Motor Insurance”, Dr. Carl Philipson includes remarks with respect to mathematical reserves. The purpose of this paper is to discuss a method of statistical estimation of Third Party Motor Insurance claim reserves. These methods can also be used for Car Damage Insurance, since reserve determination for these rapid settlement property coverages is simpler than for Third Party lines.Dr. Philipson mentions the two main purposes of claim reservesbalance sheet loss reserves which shall be estimated on the safe side for financial reasons, and those reserves needed for risk statistics. In this paper I shall confine my subject to aggregate loss reserves for financial statements and internal management operating reports.In this paper, it will be convenient to refer to both European and U.S. terminology for Motor Car and Automobile Insurance.The comparable terms are:The accident year is the important fiscal period underlying not only the statistical estimation methods discussed in this paper but it is also the basic grouping of accidents in the official reserve tests required in the Annual Statements of U.S. companies for casualty and property lines. An accident year embraces the entire population of claims incurred with accident dates in a particular calendar year, whether reported to the company in that year or subsequently (i.e., incurred /not reported).
Sur la détermination de la réserve pour sinistres en suspens dans l'assurance automobile
Authors: Molinaro Luigi 
Published: July 2016

I) Parmi les différentes questions qui se posent dans l'étude de l'assurance automobile, celle de l'évaluation des réserves techniques est sans doute une des plus importantes. Dès que l'augmentation progressive du parc des véhicules a entraîné une hausse sensible de la chiffre des affaires et que le besoin de sauvegarder l'indemnisation des sinistres de circulation a transformé la base même du rapport contractuel, le problème des garanties, indissociable de celui de la solvabilité de l'entreprise, s'est imposé à l'attention générale.En raison de cette évolution et de la nécessité d'un contrôle sur les engagements des compagnies, la fixation du montant exact de la réserve sinistres est fondamentale soit par rapport à la validité du tarif adopté (congruité des primes), soit à la possibilité de faire face aux engagements techniques moyennant des activités correspondantes. Deux aspects done d'un même problème, dont l'importance est augmentée dès que les risques se sont alourdis, les résultats de la branche défavorables, la situation économique et monétaire de plusieurs pays est devenue instable.2) Le problème du calcul de la réserve pour sinistres en cours avait été posé, il y a plus que trente ans, par M. d'Addario: dans ses études il avait mis en relief l'existence d'une relation dans l'échelonnement des paiements valable pour une période de stabilité monétaire et d'une loi de distribution par rapport à l'âge du portefeuille sinistres (génération sinistres)). A cette oeuvre, disons prioritaire, ont suivi les remarquables travaux de M. M. Thépaut, Burlot, Henry, Pellegrin, Depoid: à la lumière des données expérimentales du marché français ils ont eu le grand mérite de pousser les études sur le coût moyen des sinistres et sur la cadence des règlements.