bluuebunny/crossref_metadata_2025_split huggingface dataset:
Optimal Reinsurance and Dividend Payment Strategies
Authors: Pechlivanides Pantelis M. 
Published: July 2016

This paper presents a normative model for the sequential reinsurance and dividend-payment problem of the Insurance Company (I.C.). Optimal strategies are found in closed form for a class of utility functions. In some sense the model studied can be viewed as an adaptation of Hakansson's investment-consumption model of the individual [3] or a generalization of Frisque's model for the dynamic management of an I.C. [2].In Section 2 the model is formulated as a discrete time dynamic programming problem. The objective of the I.C. is assumed to be maximization of the expected utility of the dividend streams paid to stock/policy-holders (s/p-holders). The initial reserves level is assumed to be known. The premiums to be collected in each period for selling policies are known in advance. The losses due to claims from policy-holders are random variables independent from period to period. In each period the I.C. must decide on the portion of the reserves to be paid as dividends and on the form and level of reinsurance with a reinsurer that quotes prices for any contract.Optimal strategies in closed form are found in Section 3 when the utility function of the I.C. is given by the discounted sum of one-period utilities of dividends; and when the one-period utilities belong to the linear risk-tolerance class, which is given by: (la) u(x) = (ax + b)c+1/a(c + 1); ax + b > o, ac < o. (Ib) u(x) = log(ax + b); ax + b > o. (II) u(x) = — eγx; γ > o.
On a Form of Automobile Liability Insurance with a Prepaid Discount
Authors: Ottaviani Riccardo 
Published: July 2016

Recently two types of insurance policy covering automobile liability have become available. With this kind of policy, the insured party receives a prepaid discount on the annual premium; however, he must make an additional payment to the insurer on first report of an accident.We shall examine only one of these two types of policy, since the second is very similar to the first.On stipulation of the contract, the insured party pays a premium equal to 78 percent of that currently in force for complete coverage, depending on the various limits. However, at the same time at which the insured reports his first accident in the course of the year (and only in this case), he must make an additional payment equal to 35 percent of the premium due in the case of complete coverage. This additional payment, considered as a deposit, is repaid to the insured party if the accident has no follow up within four months; however, it may be requested again by the insurer if the case is subsequently reopened and leads to payment of damages. This additional payment will thus become a part of the premium only in the case of payment of damages for the first accident reported.In this way, the premium paid by the insured is equal to 78 percent or to 113 percent of the current premium, depending on whether or not the insured reports accidents.
Premium Rates Under Inflationary Conditions
Authors: Waters H.R. 
Published: July 2016

This short note has as its starting point an interesting article by Taylor (1979) in which he considered the effects of inflation on a risk process. Taylor showed that if the premium density increased at the same rate as the cost of individual claims then, under certain conditions, ultimate ruin was certain. This raises a natural question, viz. “If the cost of individual claims is increasing how should the premiums be increased in order to keep the probability of ruin under control ?” It is this question that we shall be considering in this note.In the next section we define the risk process that we shall be studying for the remainder of this note. Our process is essentially a compound Poisson process except that we allow the distribution function of an individual claim to depend on the time at which the claim occurs. We start the third section by deriving, with the help of a general result of Gerber (1973), a formula for the future premium density that will keep the probability of ruin for our process below a predetermined bound. We then derive a simple approximation to this formula that shows more clearly how we require the premium density to change in relation to the change in claims costs. Finally we show that if we consider the same process with annual premiums then the probability of ultimate ruin will be kept below a predetermined bound if the annual premium is calculated according to the principle of zero utility with an exponential utility function or, as a first approximation, according to the variance principle.
The Performance of Alternative Models for Forecasting Automobile Insurance Paid Claim Costs
Authors: Cummins J. David , Powell Alwyn 
Published: July 2016

When setting or modifying insurance rates on the basis of observed data, adjustments should be made for inflation between the average claim date of the observation period and the average claim date covered by policies to which the new rates will apply. In automobile insurance ratemaking in the United States, the adjustment is made as follows:where Lα = trended losses and loss adjustment expenses incurred,L0 = observed losses and loss adjustment expenses incurred during the experience period, = the predicted rate of inflation per quarter, andk = the number of quarters for which losses are being trended.The inflation coefficient, β, is an exponential growth factor that is estimated using the following equation:where = average paid claim costs for the year ending in quarter t,t = time, in quarters, t = 1, 2, …, 12, andεt = a random disturbance term.The estimation period for the equation is the twelve quarters immediately preceding the first forecast period, and the estimation is conducted utilizing ordinary least squares. Annual averages of claim costs are used as the dependent variable to smooth random and seasonal fluctuations.
Variation de la prime d'assurance de l'assistance pharmaceutique en fonction de la participation de l'assure au coût de l'assistance
Authors: Cannella Salvatore 
Published: July 2016

Un nouvel examen des normes qui régissent l'octroi des prestations d'assistance pharmaceutique semble s'imposer. En effet, l'introduction continuelle sur le marché de nouveaux produits pharmaceutiques — dont certains sont capables de juguler rapidement des formes morbides naguère lentes à guérir — et la confiance progressivement accrue que met le grand public dans des ordonnances toujours plus variées exigent, de la part des Instituts d'assurance sociale contre les maladies, des solutions permettant de répondre en même temps à des nécessités diverses: il s'agit en particulier de pouvoir autoriser l'utilisation des produits pharmaceutiques les plus modernes, capables d'accélérer la guérison des malades, même s'ils sont très coûteux, tout en évitant par ailleurs l'expansion anormale des ordonnances et en maintenant le coût de l'assistance dans les limites permises par les possibilités de financement.Le choix de la solution la meilleure est done subordonné à un ensemble de considérations sur la nécessité et la possibilité des mesures à envisager; les aspects économiques de la question ne sont pas des moindres et leur étude doit de toute évidence reposer sur des bases techniques appropriées.Il semblerait normal que ces bases techniques soient établies d'après des observations effectuées là où ces mêmes bases techniques doivent être employées; ceci n'est généralement pas possible et c'est pourquoi des éléments provenant d'autres expériences revêtent une importance particulière, ne serait-ce qu'à titre indicatif.
Optimum Structure of Trends of Activities to prevent Chance Damages
Authors: Banasinski Antoni 
Published: July 2016

In the socialist countries, where insurance — like the other primary sectors of the national economy — has been nationalized and is conducted by a single state-owned insurance company, a whole number of actuarial problems have arisen. These are problems which either did not interest the private insurance companies or else were marginal questions for them, of no great practical importance. The actuarial problems which have cropped up or have acquired particular importance in the conditions of socialist economy, include questions connected with evaluation of the efficiency of outlays for the insurance company's preventive activities intended to restrict the number and scope of chance damages). Henceforth we shall refer to expenditures of this sort as preventive outlays /expenditures/.One of the initial problems pertaining to the preventive activities of the state insurance monopoly is one which could be called the optimum structure of the trends of activities to prevent chance damages.We present the problem in the most simple form, formulating it so that it can be solved by generally-known calculus methods employed in linear programming (e.g. the simplex method given by G. B. Danzig in 1951).Let us assume that in a given period, e.g. in a year, the insurance company allocates a certain sum I for preventive purposes. Realization of these outlays is expected to reduce damage payments made by the insurance company during that period; let us call that decrease Q, the „savings” obtained by the insurance company.
Bonus ou Malus?
Authors: Gürtler Max 
Published: July 2016

Il est peu de problèmes, dans l'industrie de l'assurance, dont la solution occasionne autant de difficultés que celui consistant à fixer dans l'assurance Automobile une prime équitable du point de vue technique.On a tenté, dans plusieurs pays, de s'attaquer à ce problème par le moyen d'un bonus progressif dont bénéficierait le souscripteur n'annonçant pas de sinistre. Cependant, tant les théoriciens que les praticiens sont très partagés sur l'opportunité de cette solution.Certains mathématiciens et juristes repoussent catégoriquement le système du bonus et qualifient l'idée de la ristourne d'une partie de la prime à l'assuré n'ayant pas eu de sinistre comme étant contraire à la notion même de l'assurance. Lors d'un des derniers congrès internationaux d'actuaires, ce procédé aurait — avec un peu d'exagération — été défini comme suit: Le bonus est, en matière d'assurance, une renonciation organisée de l'assurance. Cette opinion est principalement défendue par certains actuaires franҁais ).D'autres mathématiciens, cependant, sont d'avis que le bonus est une précieuse disposition permettant, sur la base des sinistres survenus, d'évaluer chaque risque individuel plus rigoureusement que si I'on renonҁait à cette pratique). Et, à leur avis, il est inopportun de ne pas faire usage de cet élément d'information.2. “Absence de sinistres” et “Nombre de sinistres”Normalement, les primes d'assurance dépendent d'un certain nombre de facteurs caractéristiques du risque, à l'exclusion cependant des sinistres concernant un contrat particulier.
Estimation of the coefficient of variation of the excess of loss by means of Jensen's inequality for convex functions. The connection with the theory of life times
Authors: Van Klinken J. , Groenenberg C. J. 
Published: July 2016

This note deals with a way to determine upper and lower bounds for the coefficient of variation of the total claim costs in a year in excess of a certain limit value. In many a publication attention has been paid to the question of calculating, in addition to the mean of the excess costs, the variance of these costs. In this connection we only mention here the study of Vajda: Minimum Variance Reinsurance, ASTIN-Bulletin, September 1962. It is evident that in studying such problems of “statistics of large claims” the coefficient of variation, defined as the ratio of the standard deviation and the mean, may be a useful tool. If we exclude special “dangerous” claim distributions and also distributions with a very “irregular” tail, it appears possible to derive bounds for this coefficient of variation and to indicate its asymptotic behaviour. Hereby good use can be made of Jensen's inequality for convex functions. Jensen's inequality has frequently been applied to problems in the field of life insurance mathematics, but as far as the authors of this note know, not to the question mentioned here.Besides, it may have some interest to point out a connection between the question of estimating the excess of total claim costs and the theory of life times. We may translate “the limit value” as “the age already reached” and “the mean of the excess of loss” as “the expectation of life”. The estimation of the coefficient of variation ot the life time now leads to some well-known biometric formulae on life times and at the same time to an interesting observation as regards human life tables.
A Practical Statistical Method of Estimating Claims Liability and Claims Cash Flow
Authors: Clarke T.G. , Harland N. 
Published: July 2016

A few years ago Scurfield (JSS 18) indicated a method used inone U.K. non-Life Office for estimating claims liability for the Motor class of business. Since that paper was written a considerable amount of development has taken place and it is now used in the office as an effective continuous method, using computer techniques, for estimating claims liability. It has also been used for projecting expected cash flow for claims arising in the past.Whilst it is accepted that the method has limitations, it has been found that an automatic method is required especially in the production of financial models in the non-Life field, and its limitations are outweighed by the fact that there are, in our opinion, no easier methods of producing a satisfactory working model.In the following paper it is the intention to set out briefly the details of the method, then concentrating on the known limitations and the methods so far devised to combat these limitations. In the appendices we have reproduced some computer printout and figures which will provide practical information on the method.The principle behind the method is that the “Run-off” of claims payments for any “year of claim”, or similar cohort of claims, follows a particular pattern which experience has shown to be reasonably stable. We can thus study the pattern of claims payments at each stage of “run-off”, say each month and thus ascertain the average and range of values that the historic pattern shows (Fig. 1).Fig. 1.Period of delay since beginning of claims Period (Years)
Dynamic Model of Insurance Company's Management
Authors: Frisque Andre 
Published: July 2016

In this paper, we are interested in a model related to a number of periods of Company's activity.The Company calculates an amount s which then could be given as a supplementary interest to the shareholders. This calculated amount is taken from the risk reserve. Let us assume the risk reserve = S at the beginning of an operating period. If the Company gives an amount s to the shareholders, then the risk reserve is S — s. (Borch 1972; Seal 1969).We must determine the best policy of dividends, that is a rule which determines the payments to be made each year to the shareholders of the Company, maximising a definite criterion.The problem of dividends must be approached in the “dynamic programming manner”. Indeed, the payments of dividends have an effect upon further gains of the Company and its capacity to pay dividends in the future.The objective of the Company is, for example, maximising the average utility of the dividend payments, which is calculated according to the distribution of claims. (Borch 1964a; Wolff 1966).
A Note On The Multiplicative Ratemaking Model
Authors: Ajne B. 
Published: July 2016

The multiplicative ratemaking, model we have in mind is the following one. Within a certain branch of insurance we have, say for simplicity, two tarif arguments U and V. For example, in motor insurance we could think of U and V as being make of car and geographical district respectively. In fire insurance U could be class of construction for buildings and V could relate to fire defense capacities.The arguments are of a qualitative nature and argument U has r levels, while argument V has k levels. To our disposal we have statistical experience of the business for a certain period of time, consisting of—risk exposures nij (i = 1 … r, j = 1 … k).Risk exposure nij thus corresponds to the ith U-level and the jth V-level. It could be e.g. number of policy years or sum insured during the period of observation for objects belonging simultaneously to U-level i and V-level j.The nijS are known non-random quantities.—(relative) risk measures pij(i = 1 … r, j = 1 …k).Risk measure pij could be e.g. claims frequency, i.e. number of Claims divided by number of policy years, or claims cost per policy year or claims cost as a percentage of sum insured. In general pij is thus the observed number or the observed amount of claims belonging simultaneously to U-level i and V-level j, divided by the corresponding risk exposure nij.
Isotonic Optimization in Tariff Construction
Authors: Jewell W.S. 
Published: July 2016

AbstractThe problem of the best fit to set ideal values under general inequality order restrictions is examined for asymmetric, quadratic, absolute, and Chebyshev norms. Special solution procedures are given in terms of network flow algorithms over a network associated with the given isotonic order relations, and the nature of the optimal solutions is characterized for the different norms.The model is formulated in terms of finding an optimal insurance rate structure over given risk classes for which a desired pattern of tariffs can be specified. The suitability of different norms is considered in the context of corporate profitability, and the relationship to a simple rate relativities model is described.
Note on the Application of Compound Poisson Processes to Sickness and Accident Statistics
Authors: Philipson Carl 
Published: July 2016

In order to fix our ideas an illustration of the theory for (a) a general elementary random process, (b) a compound Poisson process and (c) a Polya process shall be given here below following Ove Lundberg (On Random Processes and Their Application to Accident and Sickness Statistics, Inaug. Diss., Uppsala 1940).Let the continuous parameter t* be measured on an absolute scale from a given point of zero and consider the random function N* (t*) which takes only non-negative and integer values with N* (o) = o. This function constitutes a general elementary random process for which the conditional probability that N* (t*) = n relative to the hypothesis that shall be denoted , while the absolute probability that N* (t) = n i.e. shall be written If quantities of lower order than dt* are neglected, we may write for the conditional probability that N* (t* + dt*) = n + 1 relative to thehyp othesis that N* (t*) = n, i.e. is the intensity function of the process which is assumed to be a continuous function of t* (the condition of existence for the integral over the given interval of t* for every n > m may be substituted for the condition of continuity). The expectations for an arbitrary but fix value of t* of N* (t*) and p* (t*) will be denoted by the corresponding symbol with a bar so thatIf is uniformly bounded for all n in the interval o ≤ t* < T*, where T* is an arbitrary but fix value of t*, we have i.a. that
Sur les événements en chaîne et la distribution binomiale négative généralisée
Authors: Campagne Cornelis 
Published: July 2016

Dans plusieurs études [1] Ammeter a démontré que la distribution binomiale négative généralisée peut être interprétée de différentes manières, à savoir commea. une contagion des probabilités (Pólya-Eggenberger);b. une distribution de Poisson basée sur des probabilités fondamentales variables;c. une distribution de Poisson où la probabilité fondamentale de sinistres n'est pas suffisamment connue;d. une distribution de Poisson par rapport aux événements, où un seul événement peut comporter plusieurs prétentions de sinistres;e. une distribution de Poisson basée sur une modification de la répartition des montants de sinistres.On a, en effet, les relations suivantes:a. la contagion des probabilitésoù F(x, P, h, p(z)) représente la probabilité que le sinistre est au plus égal à x dans un intervalle de temps où le sinistre probable est P. x et P y sont exprimés en le sinistre moyen par événement. p(z)dz est la fonction de fréquence du sinistre par événement.Nous posons est la convolution de p(z) avec p(z), faite r fois, tandis que h est la notation du paramètre qui figure dans la distribution binomiale négative. Si h est égal à ∞ nous obtenons comme fonction de répartition pour le nombre d'événements survenus la distribution de Poisson.
Assurances Automobiles et Revenus Financiers
Authors: Sousselier Jean 
Published: July 2016

La question est controversée de savoir si l'on doit tenir compte du revenu des placements — et éventuellement des bénéfices sur réalisations de valeurs — pour apprécier le résultat technique de la branche Automobiles.Rappelons qu'en France, réglementairement, dans les états B3 qui font apparaître le résultat technique de la catégorie, on tient compte des frais généraux, ce qui est normal, mais non des intérêts.En réalité, il semble bien qu'il soit difficile de faire abstraction d'un élément non négligeable de profits et pertes qui dérive de l'exercice même de l'industrie de l'Assurance, mais la question demeure de savoir dans quelle mesure il faut en tenir compte.Nous allons montrer que la question est intimement liée à la conception même que l'on se fait du montant des réserves techniques à inscrire au passif du bilan.On ne peut avoir une idée saine tant des résultats techniques que des revenus de placements que si la comptabilité est établie par exercice de souscription. C'est l'hypothèse que nous retiendrons dans ce qui va suivre).Un tel exercice donne lieu à encaissement d'un certain montant de primes, au paiement de commissions et de frais généraux et enfin au paiement de sinistres s'échelonnant dans le temps, au delà de la clôture calendrier de l'exercice.Pour plus de rigueur même — et l'on peut se référer au mode de raisonnement appliqué en Assurance sur la Vie — il faut considérer séparément les différentes échéances de primes, chacune se comportant comme une sorte d'exercice isolé: ensemble des assurances à échéance du Ier janvier, ensemble des assurances à échéance du 2 janvier, etc… jusqu'à celles à échéance du 31 décembre. (Il est indifférent de raisonner sur un ensemble ou „en valeur probable” selon le principe actuariel classique).
Colloque Astin 1963 de Trieste Rapport introductif sur le 2e thème, parties b et c
Authors: Sousselier Jean 
Published: July 2016

Ce sujet n'a pas été traité, peut-être parce qu'il paraît trop simple; pourtant il mérite examen vu son utilité pratique certaine.Il est impossible de négliger le jeu de la réserve de Risques en Cours dans l'estimation du taux des sinistres c'est-à-dire dans l'ap-préciation de la tarification et de l'équilibre d'une branche d'assurances.D'autre part, comme le souligne justement la note introductrice aux thèmes proposés établie par le Comité Astin, le problème est moins immédiat qu'il ne paraît:On considère généralement la réserve de Risques en Cours (l'expression anglaise risques non expirés est peut-être meilleure) comme un simple pourcentage des primes totales: c'est la fraction de primes non acquise à l'exercice mais ceci suppose que le risque est uniformément réparti dans le temps et que les primes correspondent exactement aux risques couverts.En fait deux conceptions sont possibles:— méthode rétrospective: on considère le déroulement passé des opérations: schématiquement on prend la différence entre les primes perҁues et les sinistres survenus; ce qui hypothèque l'avenir.— méthode prospective: on fixe la somme nécessaire pour faire face aux sinistres à venir dans l'intervalle de temps encore couvert par les polices en cours, ceci compte tenu du taux actuel de sinistres et même de son évolution probable dans le futur immédiat.La méthode prospective est-elle plus correcte? Il peut le sembler. Mais c'est seulement viser à l'équilibre probable du bilan futur, au détriment du bilan actuel. Pourquoi une insuffisance de tarification, par exemple, doit-elle peser sur le seul compte de l'exercice clos?