bluuebunny/crossref_metadata_2025 huggingface dataset:
A Model of the Unmet Need for Cleft Lip and Palate Surgery in Low‐ and Middle‐Income Countries
Authors: Carlson Lucas C. , Stewart Barclay T. , Hatcher Kristin W. , Kabetu Charles , VanderBurg Richard , Magee William P.
Published: July 2016

Background

There is a significant unmet need for the cleft lip and/or palate (CL/P) care in low‐ and middle‐income countries (LMICs)
; however, country‐level estimates that can be used to inform local and international cleft care program strategies are lacking.

Methods

Using data from Operation Smile surgical programs in twelve LMICs and country‐level indicators from the World Health Organization and World Bank, we developed a model to estimate the proportion of individuals with CL/Ps older than respective surgery age targets for cleft lip and cleft palate surgery (1 and 2 years, respectively). After extrapolating this model to other LMICs with available indicator data, we combined these findings with estimates of CL/P prevalence among live births to estimate the total number of unrepaired CL/P cases in LMICs worldwide.

Results

The models were constructed from a total of 887 cases of cleft palate and 576 cases of cleft lip across the twelve countries. From these, we estimated that there are 616,655 cases of unrepaired CL/P (95 % CI 564,893–678,503) in the 113 countries with available data for extrapolation. The rate of unrepaired CL/Ps ranged from 2.5 per 100,000 population in Romania to 28.5 per 100,000 in Cambodia, respectively (median rate 10.7 per 100,000 population).

Conclusions

Our model provides marked insight into the global surgical backlog due to cleft lip and palate. While the most populated LMICs have the largest number of unrepaired CL/Ps, low‐income countries with relatively less healthcare infrastructure have exceptionally high rates (e.g., Cambodia, Afghanistan, and Nepal). These estimates can be used by local and international cleft care organizations to set program priorities, estimate resource requirements, and inform strategies to support cleft care.
P123 assisted synthesis and characterization of urchin-like γ-Al2O3 hollow microspheres
Authors: Liang Qi , Guo Xiaorui , Quan Tingting , Meng Fancheng
Published: July 2016

Hierarchical urchin-like γ-Al2O3 hollow microspheres were prepared by a hydrothermal method followed by a calcination process using Al(NO3)3·9H2O as aluminum source, NH3·H2O as precipitating agent, and P123 as structure-directing agent (SDA). The obtained samples were investigated using X-ray diffraction (XRD), filed emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), and N2 adsorption/desorption. The influences of P123 concentration, acidic condition, and hydrothermal time on the morphology of product were discussed. P123 has a great influence on ruling the oriented attachment of nanowires and stabilizing the superstructure in the self-assembly process. The 3D urchin-like hollow microspheres have a surface area of 210.2 m2/g and the average pore size is 11.42 nm, which have widely potential application such as catalyst, adsorption, and separation.
Nonlinear Frequency Response Analysis and Jump Avoidance Design of Molecular Spring Isolator
Authors: Yu M.-C. , Gao X. , Chen Q.
Published: July 2016

Molecular spring vibration isolation technology has been invented in the recent years but it still needs further development in dynamics theory. A molecular spring isolation (MSI) consists of water and hydrophobic zeolites as working medium, providing high-static-low-dynamic stiffness. The dynamic properties of MSI are thoroughly investigated in this paper. Firstly, the nonlinear dynamic model of a vibration system support by MSI, i.e. the equation of motion, is established. Then the averaging method is employed to estimate the frequency response function (FRF) of the primary resonance. The phase trajectories diagram evolvement of primary resonance is also investigated to analysis the stability of the primary resonance response. From the plot of FRF, it is found that there exists a jump phenomenon induced by nonlinear stiffness, which may have harmful impacts on the equipment which is supposed to be protected from vibrations and shocks. To avoid jump, the FRF is analyzed to find the critical values of system parameters and a jump avoidance criterion is introduced.
Party System Volatility in Post-Communist Europe
Authors: Crabtree Charles , Golder Matt
Published: July 2016

In their 2014 article in the British Journal of Political Science, Eleanor Neff Powell and Joshua A. Tucker examine the determinants of party system volatility in post-communist Europe. Their central conclusion is that replacement volatility – volatility caused by new party entry and old party exit – is driven by long-term economic performance. This article shows that this conclusion is based entirely on a miscalculation of the long-term economic performance of a single country, Bosnia-Herzegovina. The study’s reanalysis suggests that little is known about what causes party system volatility in post-communist Europe. Given the negative consequences traditionally associated with party system volatility, this area of research cries out for new theoretical development.
Schellenberg's evolutionary religion: how evolutionary and how religious?
Authors: ROTTSCHAEFER WILLIAM A.
Published: July 2016

InEvolutionary Religion, J. L. Schellenberg synthesizes his previous impressive contributions to an understanding of religion by formulating an account of religion supported by a Darwinian evolutionary theory understood as a science of the deep future. Such a future enables the realization that our present understandings of religion are immature, that future understandings of divine reality may be radically altered and that religious practice may become the centre of human well-being. In this article, I argue that Schellenberg's evolutionary religion represents at best but half the evolutionary story, its epistemic side. Ontologically, it remains fundamentally non-evolutionary. Positively, I suggest naturalistic alternatives to Schellenberg's Ultimate. I conclude that Schellenberg's evolutionary religion is neither adequately evolutionary nor adequately religious.
Cooperative Empires: Provincial Initiatives in Imperial Austria
Authors: Osterkamp Jana , Hyland Jaime
Published: July 2016

The title “Cooperative Empires” may seem contradictory—or even provocative—to many historians of empire. It is widely believed that one of the defining characteristics of an empire is the presence of little or no cooperation among its individual provinces. More than that: there is a deliberate separation between the provinces that can go so far as to become a prohibition against cooperation. In theory, at least, each province must communicate with the imperial center, but not with other provinces. This contradiction between empire and cooperation is neatly illustrated by a true family story. The story is set in the 1970s in Prague, on the western edge of that space that historians today describe as the Soviet Empire. My mother, an East German from East Berlin, was then working as an interpreter in Prague. She was sitting on the tram on the way to visit some Czech friends who shared her love of jazz music. A queasy feeling began to come over her as she recalled that she was in fact forbidden to visit Czech friends, precisely because she was working in the German Democratic Republic's (GDR) embassy in Prague. It suited both the Soviet Union and the GDR that their foreign workers should not come into private contact with other nationalities, even if they belonged to allied fraternal countries. This was a sort of socialist version of the “divide and rule” principle as it was practiced in the nineteenth century.
Agroforestry in Bolivia: opportunities and challenges in the context of food security and food sovereignty
Authors: JACOBI JOHANNA
Published: July 2016

Agroforestry systems have long been implemented in Bolivia, but little is known about their overall current status. Interviews with farmers, policymakers and members of civil society organizations about the challenges and opportunities that agroforestry faces, as well as field visits to agroforestry projects revealed a wide range of agroforestry initiatives in Bolivia that provide ecosystem services, food and income to local families. All interviewees attributed a high potential to agroforestry, for example, to promote biodiversity, water conservation, food sovereignty and adaptation to climate change impacts. However, agroforestry initiatives lacked support because government incentives were channelled to cattle rearing and large-scale monocultures rather than diversified farming systems, and agroforestry initiatives tended to be small and isolated. A nationwide policy is needed which is coordinated with civil society organizations and individual farmers and strategically and efficiently supports agroforestry initiatives – especially in the most vulnerable first years of establishment – through extension services and access to materials, markets, knowledge and financial resources.
Recent Developments in Economic Theory and their Application to Insurance
Authors: Borch Karl
Published: July 2016

The very title of this paper may cause some surprise, since economic theory so far has found virtually no application in insurance. Insurance is obviously an economic activity, and it is indeed strange that general economic theory should seem inapplicable to insurance.

This apparent paradox may to some extent be explained by the historic development. Actuarial mathematics and the essential scientific basis of insurance were developed into a self-contained and fairly complete theory long before economists could claim the name of science for their subject. Actuaries and other insurance people may from time to time have turned to economic theory for help on their problems. In most cases they must have turned away in disappointment, being convinced that actuarial mathematics was well ahead of general economic theory.

The last point is brought out clearly in a paper on the safety loading of insurance premiums which Tauber (19) presented at the Sixth International Congress of Actuaries in Vienna in 1909. In the introduction to this paper Tauber seems to consider risk bearing as a service and appears to assume that it like all other goods and services must have a price, determined by supply and demand in the market. Tauber did not develop this idea, apparently because the economic theory of his time was utterly unable to analyse the problem. That his approach was sound, and that the problem can be formulated and solved by modern economic theory, has been indicated in a previous paper (6).

During the last thirty years there has been an extremely rapid development in economic theory. The “General Theory” of Keynes (12) which appeared in 1936, is usually considered to have caused a revolution in economic theory. However, this “revolution” has not lead to any developments which seem to have an immediate application in insurance. Post- and pre-Keynesian economics are equally powerless when confronted with the problem which Tauber tried to formulate. It is therefore premature to conclude from the title of this paper that economic theory has caught up with actuarial science, and that the theory of insurance has now become a part of a general theory comprising all economic activities.
The Ruin Problem with a Finite Time Horizon
Authors: Amsler Marc-Henri
Published: July 2016

The paper presents an extension of the classical Cramér–Lundberg ruin theory: the famous upper bound for the ruin probability with an infinite time horizon can be extended in a certain sense to the short and middle term case. Furthermore, a relation between the average values of lifetime and ruin amount is given.
A Note on Iterative Premium Calculation Principles
Authors: Goovaerts M. J. , Vylder F. De
Published: July 2016

Gerber (1974) has given a characterization of the exponential utility function by proving the fact that a premium calculation principle of zero utility is iterative iff the underlying utility function is linear or exponential. In the present note we prove the more general result that the premium calculation principle introduced by Bühlmann, Gagliardi, Gerber and Straub (1977) is iterative iff the underlying function v is linear or exponential or when the principle is a mean value principle.
On the Statistical Estimation of Costs of Claims
Authors: Ajne B.
Published: July 2016

For a number of reasons it is important for an insurance company to estimate the claims costs of a year within the different branches of non-life insurance as soon as possible after the end of the year. The claims cost of a year is hereby defined as the total cost, before taking reinsurance into account, of all claims generated by events that have occurred during the year. When the estimation has to be done, part of these claims will be reported and closed, others will be reported and still open, and the remaining ones will be incurred but not yet reported. The total cost of the claims is defined as the sum of all payments that have been made or will be made on account of the claims. Thus, in this definition no regard is paid to interest, i.e. no discount factors are applied to payments to be made in the future.

Instead of considering a year, we could consider an arbitrary period of twelve consecutive months. The estimation problem is the same, and estimates of the claims costs of consecutive twelve months periods will allow a closer following up of trends and yield predictions for the present year.

For estimates to be available quickly, it is necessary that the estimation procedure be founded on data that are available immediately at the end of the year or the latest twelve months period. This means a.o. that for the bulk of the open claims, individual estimates of reserves by claims adjusters are out of the question. In other words, the estimation procedure has to be basically of a statistical character. In addition, for continuous estimates to be produced it has to be well adapted to electronic data processing. Indata to the procedure have to be stored in the memories of the computer.
Windstorm Coverage in Japan
Authors: Wakuri Masao
Published: July 2016

Japan is not only a well-known earthquake prone country, but also a land very liable to damage by windstorm, flood, tidal wave and highwater. Especially, it is visited every year by typhoons or tropical cyclones. These occur during the period from early summer to autumn with accompanying heavy rains, and severe damage is often suffered. Most of the serious disasters result from the following causes.

a) Flood from a rapid small river in mountainous areas or landslide occurring there.

b) Innundation of a large plain area caused by the collapse of embankments following heavy rain.

c) Highwater or tidal wave in a harbour or a bay, which is often caused by the visit of a typhoon particularly at full tide.

Generally speaking, damage by the wind is much less in severity than that by flood, tidal wave or highwater.

These natural calamities occur every year, but the extent of the damage differs greatly from year to year. Taking an example of the damage to buildings and contents during 10 years from 1965 to 1974, the largest annual damage estimated for the whole country was ¥ 161.875 million (approx. U.S. $ 578 million), the smallest ¥ 9.398 million (approx. U.S. $ 33,6 million) and the average ¥ 58.561 million (approx. U.S. $ 209 million). (These are the original figures not adjusted for inflation. Also, they do not include the damage to outdoor objects such as roads, bridges, railways, communication facilities, electricity facilities and farms). The greatest windstorm damage in recent years was brought about by the “Bay of Ise Typhoon” in September 1959, at which 153.893 buildings were lost or seriously damaged, 5.101 persons were killed or went missing and 2.430 ships were lost.
Largest Claims Reinsurance (LCR). A Quick Method to Calculate LCR-Risk Rates from Excess of Loss Risk Rates
Authors: Benktander G.
Published: July 2016

Let us denote by E(x) the pure risk premium of an unlimited excess cover with the retention x and by H(x) and m(x) the corresponding expected frequency and severity.

We thus have E(x) = H(x) · m(x).

H(x) is a non-increasing function of x and for practical purposes we can assume that it is decreasing; H′(x) < o. The equation H(x) = n has then only one solution xn, where n is a fixed integer.

Let En denote the risk premium for a reinsurance covering the n largest claims from the bottom.

Let us define Intuitively we feel that is a good approximation for En.

We shall first show that when the claims size distribution is Pareto and the number of claims is Poisson distributed, is a good approximation for En, being slightly on the safe side. We further include a proof given by G. Ottaviani that the inequality always holds.

In the Pareto case we have

where the Poisson parameter t stands for the expected number of claims in excess of 1 (equal to a suitably chosen monetary unit) and

.
A Numerical Illustration of Optimal Semilinear Credibility
Authors: De Vylder Fl. , Ballegeer Y.
Published: July 2016

The homogeneous (in time) model of credibility theory is defined by a sequence Θ, X1, X2, … of random variables, where for Θ = θ fixed, the variables X1, X2, … are independent and equidistributed. The structure variable Θ may be interpreted as the parameter of a contract chosen at random in a fixed portfolio, the variable Xk as the total cost (or number) of the claims of the kth year of that contract.

Bühlmann's linear credibility premium of the year t + 1 may be written in the form

where f is a linear function. In optimal semilinear credibility, we look for an optimal f, not necessarily linear, such that (1) is closest to Xt+1 in the least squares sense. In the first section we prove that this optimal f, denoted by f*, is solution of an integral equation of Fredholm type, which reduces to a system of linear equations in the case of a finite portfolio. That is a portfolio in which Θ and Xk can assume only a finite number of values.

In the second section we see that the structure of such a portfolio is closely connected with the decomposition of a quadratic form in a sum of squares of linear forms.

In the last section we calculate numerically the optimal premium for a concrete portfolio in automobile insurance. We limit ourselves to the consideration of the number of claims. The optimal premium is compared with the usual linear premium. The difference is far from negligible.
Optimal Claim Decisions for a Bonus-Malus System: a Continuous Approach
Authors: De Pril Nelson
Published: July 2016

For the premium calculation the insurer will split up his collectivity of risks into risk groups which are homogeneous with respect to some directly observable risk factors. All risks of such a risk group will be charged the same base premium. But it is clear that by such an a priori classification not all determined factors can be taken into consideration, so that there will still remain accident proneness differentials within a risk group. Since these differentials will be reflected in the course of time by the claim experience of each risk, the insurer can come to a fair tarification by adjusting, each period, the base premium according to the individual claim experience of the risk. Such a system in which earlier neglected risk factors are taken into account a posteriori is an individual experience rating system. Our main interest goes to the following side-effect of experience rating: since an unfavourable claim experience results in a premium increase, an experience rated policyholder is stimulated to self-insure small damages. This phenomenon is well know in connection with bonus-malus systems in motor-car insurance, which explains why it is called “bonus-hunger”.

In the present paper a continuous time model for the bonus-malus system is set up which takes into account this hunger for bonus. An insured causing an accident will decide according to a certain decision rule whether to file a claim with his insurance company. The relevant information that he needs to make this decision is: his current risk class, the number of claims he has already filed during that period and the moment at which the decision is to be made.
A Game Theoretic Look at Life Insurance Underwriting
Authors: Lemaire Jean
Published: July 2016

The decision problem of acceptance or rejection of life insurance proposals is formulated as a two-person non cooperative game between the insurer and the set of the proposers. Using the minimax criterion or the Bayes criterion, it is shown how the value and the optimal strategies can be computed, and how an optimal set of medical informations can be selected and utilized.
The Effect of Reinsurance on the Degree of Risk Associated with an Insurer's Portfolio
Authors: Andreadakis M. , Waters H. R.
Published: July 2016

There are many reasons why an insurer may choose to reinsure a part of his portfolio (see, for example, Carter (1979, p. 5 ff.)) and many ways in which he can assess the effectiveness of the reinsurance arrangements he makes. In this paper we assume the insurer wishes to reinsure a part of his portfolio in order to reduce its “riskiness”. We take as given a portfolio consisting of n independent risks together with the total premium charged to insure these risks and we investigate the effect on the degree of risk associated with the portfolio (see §3 for a definition) of varying the excess of loss or proportional reinsurance limits for each risk.

We are given an insurance portfolio consisting of n independent risks. A risk may consist of a single policy or a group of policies: the essential points being that a reinsurance limit, either excess of loss or proportional, is the same for all claims arising from a particular risk, although reinsurance limits may vary from one risk to another. We assume the claims arising from each risk have a compound Poisson distribution. To be more precise, we assume the number of claims arising from the i-th risk is a Poisson process with mean Pi claims each year and the size of each claim has distribution function Fi. As usual, the size of a claim is independent of the time at which it occurs and of all other claims. We also assume that Fi(O) = O for each i, so that we consider only positive claims amounts. We take as given the total annual premium, P, charged by the insurer in respect of these risks. We make no assumption about the way in which P is calculated but we do assume that
The Core of a Reinsurance Market
Authors: Baton Bernard , Lemaire Jean
Published: July 2016

In a series of celebrated papers, K. Borch characterized the set of the Pareto-optimal risk exchange treaties in a reinsurance market. However, the Pareto-optimality and the individual rationality conditions, considered by Borch, do not preclude the possibility that a coalition of companies might be better off by seceding from the whole group. In this paper, we introduce this collective rationality condition and characterize the core of this game without transferable utilities in the important special case of exponential utilities. The mathematical conditions we obtain can be interpreted in terms of insurance premiums, calculated by means of the zero-utility premium calculation principle. We then show that the core is always non-void and conclude by an example.
The Esscher Premium Principle: A Criticism
Authors: Zehnwirth Benjamin
Published: July 2016

The Esscher premium principle has recently had some exposure, namely, with the works of Bühlmann (1980) and Gerber (1980).

Bühlmann (1980) devised the principle and coined the name for it within the framework of utility theory and risk exchange. Geruber (1980), on the other hand, gives further insight into the principle by studying it within the realm of forecasting in much the same spirit as credibility theorists forecast premiums. However, there is an important distinction: the choice of loss function.

The present note sets out to criticize this relatively embryonic principle using decision theoretic arguments and indicates that the Esscher premium is essentially a small perturbation of the well established linearized credibility premium Bühlmann (1970).

Let H denote the Esscher premium principle with loading h > o. That is, if X is an observable random variable and Y is a parameter (a risk or a random quantity) to be forecasted then the Esscher premium is given by

That is, H(Y ∣ X) is the Bayes decision rule for estimating Y given the data X relative to the loss function

where a is the estimate of Y, and of course the loading h is greater than zero.

Now, for the clincher. This loss function is nonsensical from the point of view of estimation. It indicates a loss (or error) to the forecaster that is essentially the antithesis of relative loss.
Bounds on Modified Stop-Loss Premiums in Case of Known Mean and Variance of the Risk Variable
Authors: De Vylder F. , Goovaerts M. , De Pril N.
Published: July 2016

In case of a stop-loss treaty the reinsurer takes over that part of the risk that exceeds a given amount y1. We will deduce bounds on a modified stop-loss treaty where the liability of the reinsurer is limited to y2–y1 in case the claim amount exceeds y2. Upper and lower bounds of this modified stop-loss premium are obtained as a simple application of results obtained earlier by the first author.
Une méthode pour calculer une ristourne adéquate pour années sans sinistres
Authors: Bichsel F.
Published: July 2016

En Suisse, les sociétés d'assurances bonifient à leurs assurés en responsabilité civile autos une ristourne qui dépend du nombre des années sans sinistres, suivant le barème ci-après:

Cette ristourne a pour but de tenir compte des facteurs d'ordre subjectif qui influencent le risque et qui ne peuvent être pris en considération dans les tarifs.

Les deux questions suivantes se posent:

A) Y a-t-il en réalité des différences dans le risque subjectif justifiant la bonification d'une ristourne pour années sans sinistres?

B) Si oui, le barème indiqué ci-haut tient-il compte de ces différences d'une façon adéquate?

Le présent travail a pour but de répondre à ces deux questions en appliquant les méthodes modernes des tirages au sort.

Question A

Voici les résultats de quelques tirages au sort du portefeuille de „La Générale de Berne”

S'il n'y avait pas de différences dans le risque subjectif, la variable aléatoire k devrait suivre la distribution de Poisson. Toutefois, on sait que dans ce cas, devrait être égal à s2(k), ce dont il n'est évidemment pas question pour les chiffres ci-dessus. En conséquence, k n'est pas distribué d'après Poisson, et l'existence de différences dans le risque subjectif est prouvée.

On pourrait se demander si les différences entre et s2(k) sont de nature aléatoire. Une investigation spéciale a toutefois montré que si k suivait la distribution de Poisson, la probabilité pour des différences aussi élevées que celles des tirages indiqués ci-haut serait pratiquement nulle.
Experience rating and credibility
Authors: Bühlmann Hans
Published: July 2016

Let me begin with some practical examples of experience rating.

a) Swiss Automobile Tariff 1963

— Within each tariff-position there are 22 grades:

— The new owner of a car starts at grade 9

— The basic premium is determined on the basis of objective characteristics of the risk and essentially depends on the horse-power classification of the car

— The 22 grades are experience-rated as follows: For each accident one rises three grades and for each accident-free year one falls one grade. A driver who has I accident in every 4 years hence remains within four adjacent grades.

b) Sliding Scale Premiums in Reinsurance

Excess of Loss Contracts often stipulate that:

The rate of premium to be applied to the subject premium volume is determined at the end of the cover period as follows:

subject to a minimum of 0,04

and a maximum of 0,08

c) Participation in Mortality Profit in Group Life Insurance

A group life insurance covers the members of the group on a one year term basis. It is often agreed that at the end of the year mortality profits are given back to the group according to the formula

refund = x% gross premiums — y% claims (where x < y)

All these examples fall under the heading “Experience Rating”. What do they have in common?

Definition: A system by which the premium of the individual risk depends upon the claims experience of this same individual risk.
The optimal reinsurance treaty
Authors: Borch Karl
Published: July 2016

1. Some years ago I discussed optimal reinsurance treaties, without trying to give a precise definition of this term [1]. I suggested that a reinsurance contract could be called “most efficient” if it, for a given net premium, maximized the reduction of the variance in the claim distribution of the ceding company. I proved under fairly restricted conditions that the Stop Loss contract was most efficient in this respect.

I do not consider this a particularly interesting result. I pointed out at the time that there are two parties to a reinsurance contract, and that an arrangement which is very attractive to one party, may be quite unacceptable to the other.

2. In spite of my own reservations, it seems that this result —which I did not think deserved to be called a theorem—has caused some interest. Kahn [4] has proved that the result is valid under far more general conditions, and recently Ohlin [5] has proved that the result holds for a much more general class of measures of dispersion.

In view of these generalizations it might be useful to state once more, why I think the original result has relatively little interest. In doing so, it is by no means my purpose to reduce the value of the mathematical generalizations of Kahn and Ohlin. Such work has a value in itself, whether the results are immediately useful or not. I merely want to point out that there are other lines of research, which appear more promising, if our purpose is to develop a realistic theory of insurance.
Modern Portfolio Theory: Some Main Results
Authors: Müller Heinz H.
Published: July 2016

This article summarizes some main results in modern portfolio theory. First, the Markowitz approach is presented. Then the capital asset pricing model is derived and its empirical testability is discussed. Afterwards Neumann–Morgenstern utility theory is applied to the portfolio problem. Finally, it is shown how optimal risk allocation in an economy may lead to portfolio insurance.
Experience Rating and Credibility
Authors: Bühlmann Hans
Published: July 2016

Classical statistics deals with the following standard problem of estimation:

Given: random variables X1, X2 … Xn independent, identically distributed, and

observations x1, X2 … xn,

Estimate: parameter (or function thereof) of the distribution function common to all Xi.

It is not surprising that the “classical actuary” has mostly been involved in solving the actuarial equivalent of this problem in insurance, namely

Given: risks R1R2 … Rn no contagion, homogeneous group,

Find: the proper (common) rate for all risks in the given class.

There have, of course, always been actuaries who have questioned the assumptions of independence (no contagion) and/or identical distribution (homogeneity). As long as ratemaking is considered equivalent to the determination of the mean, there seem to be no additional difficulties if the hypothesis of independence is dropped. But is there a way to drop the condition of homogeneity (identical distribution)?
Reciprocal Reinsurance Treaties
Authors: Borch Karl
Published: July 2016

In this paper we shall study the situation of two insurance companies which are negotiating with the view of concluding a reciprocal reinsurance treaty. We assume that the two companies are under no compulsion to reach an agreement. This means that if the companies conclude a treaty, the treaty must be such that both companies consider themselves better off than without any treaty. We futher assume that no third company can break into the negotiations. This means that the two companies either have to come to terms, or be without any reinsurance.

How the two parties reach an agreement in a situation like this, is one of the classical problems of theoretical economics. It is usually referred to as the “Bargaining Problem”. The problem appears very simple, but this is a deception. It has proved extremely difficult to formulate generally acceptable assumptions which give the problem a determinate solution. The “Theory of Games”, developed by von Neumann and Morgenstern (10), does not give a determinate solution, but it has greatly increased our understanding of such problems, and the present paper will draw heavily on that theory.

The situation which we propose to study, is very simple, may be too simple to have any bearing on reinsurance negotiations in real life. If there exists a reinsurance market, which also is a perfect market in the sense given to this term in economic theory, bartering between two companies does not make any sense. They could both do equally well or better by dealing in the market at the market price.
Two Studies in Automobile Insurance Ratemaking
Authors: Bailey Robert A. , Simon LeRoy J.
Published: July 2016

Section A of this paper uses the Canadian experience for private passenger automobiles to show (1) that merit rating is almost as effective as the class plan in separating the better risks from the poorer risks, (2) that both merit rating and class rating leave unanalyzed a considerable amount of variation among risks and (3) that certain available evidence supports the conclusion that annual mileage, which has long been felt to be an important measure of hazard, is a very significant cause of this unanalyzed variation among risks.

Section B presents a method for obtaining relativities among groups on which a multiple classification system has been imposed. The customary method of calculating class relativities uses the total experience for each class with all subdivisions within the classes added together. With the customary method it is difficult to make a completely accurate adjustment for different distributions by territory or merit rating, because any change in the class relativities disturbs the other sets of relativities and conversely. It is shown that even if such an adjustment were made, the customary method of calculating relativities one set at a time does not reflect the relative credibility of each subgroup and does not produce the best fit to the actual data. Moreover it produces differences between the actual data and the fitted values which are far too large to be caused by chance. In addition, for private passenger automobile insurance in Canada, it is shown that two sets of relativities which are multiplied together cannot produce the best fit to the actual data, and some of the consequences of trying to do so are explained. Some methods are advanced whereby all sets of relativities for classes, merit ratings, territories, and so forth, can be calculated simultaneously, which will overcome all the deficiencies in the customary method. These improved methods use the technique of minimizing a measure (technically known as the chi-square test) of the differences between the actual data and the fitted values. Some applications to other lines of insurance are mentioned.
The Utility Concept Applied to the Theory of Insurance
Authors: Borch Karl
Published: July 2016

In some recent papers ((1), (2) and (3)) about reinsurance problems I have made extensive use of utility concepts. It has been shown that if a company follows well defined objectives in its reinsurance policy, these objectives can be represented by a utility function which the company seeks to maximise. This formulation of the problem will in general make it possible to determine a unique reinsurance arrangement which is optimal when the company's objectives and external situation are given.

More than 50 years ago Guldberg (4) wrote (about the probability of ruin): “Wie hoch diese Wahrscheinlichkeit gegriffen werden soil, muss dent subjektiven Ermessen oder von Aussen kommenden Bedingungen überlassen bleiben”. This is the traditional approach to reinsurance problems. It does obviously not lead to a determinate solution. Most authors taking this approach conclude their studies by giving a mathematical relation between some measure of “stability”, such as the probability of ruin, and some parameter, for instance maximum retention, to which the company can give any value within a certain range. Such studies do usually not state which particular value the company should select for this parameter, i.e. what degree of stability it should settle for. This question is apparently considered as being outside the field of actuarial mathematics.
Some Remarks on a Recent Paper by Borch
Authors: Kahn Paul Markham
Published: July 2016

In his recent paper, “An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance”, presented to the XVIth International Congress of Actuaries, Dr. Karl Borch considers the problem of minimizing the variance of the total claims borne by the ceding insurer. Adopting this variance as a measure of risk, he considers as the most efficient reinsurance scheme that one which serves to minimize this variance. If x represents the amount of total claims with distribution function F (x), he considers a reinsurance scheme as a transformation of F (x). Attacking his problem from a different point of view, we restate and prove it for a set of transformations apparently wider than that which he allows.

The process of reinsurance substitutes for the amount of total claims x a transformed value Tx as the liability of the ceding insurer, and hence a reinsurance scheme may be described by the associated transformation T of the random variable x representing the amount of total claims, rather than by a transformation of its distribution as discussed by Borch. Let us define an admissible transformation as a Lebesgue-measurable transformation T such that

where c is a fixed number between o and m = E (x). Condition (a) implies that the insurer will never bear an amount greater than the actual total claims. In condition (b), c represents the reinsurance premium, assumed fixed, and is equal to the expected value of the difference between the total amount of claims x and the total retained amount of claims Tx borne by the insurer.
On Optimal Properties of the Stop Loss Reinsurance
Authors: Pesonen Erkki
Published: July 2016

Let F(x) be the distribution function of the total amount ξ of claims of an insurance company. It is assumed that this company reduces its liability by means of one or several reinsurance arrangements. Let the remaining part of claims amount be equal to η, which is another random variable. Reinsurance arrangements are supposed to fulfil the following consistency condition: if ξ = x, then almost certainly o ≤ η ≤ x. Presumably all reinsurance arrangements occuring in practice can be supposed to fulfil this requirement.

The problem is to find an optimal reinsurance arrangement, i.e. an optimal random variable η, in the sense that, the net reinsurance premium being given, the variance of η reaches its minimum. In other words, a variable η is looked for, which gives

E{η} = P = const.; V{η} = minimum

In the sequel we use conditional expectations in the sense defined by DOOB ([I]).

Let η be an arbitrary random variable satisfying the consistency condition. If

R(x) = E{η|ξ =x},

then evidently ≤ R(x) ≤ x. Further we have

For the variance the inequality

holds true, since

Clearly the arrangement E {η|ξ} gives also to the reinsurer a smaller variance than the original arrangement.
The Assessment of Solvency
Authors: Stewart Colin M.
Published: July 2016

Effectively, a non-life insurance concern may be considered to be solvent if the supervisory authorities of the country or countries in which it operates allow it to continue operating. It is of no avail to claim that, by some other criterion, the concern may be considered to be solvent; it is by reference to the controls imposed by supervisory authorities that the concern must operate. For this reason, it is apposite to consider the principles of solvency assessment in the context of the financial statements and other documents generally available to supervisory authorities, as distinct from the theoretical mathematical concepts underlying insurance operation.

The primary purpose of supervision is to make sure that a concern does not enter into obligations which it will be unable to fulfil. It is thus essentially a dynamic standard, not a static one having regard only to the business already accepted, but the first requirement is nevertheless to test the concern's finances in relation to the business already on the books. If this test is passed, then at least it is known that the concern will not be depending upon profits from new business and renewals to help to meet the cost of its present liabilities.

This raises the question of what controls might be applied to new business. The two main types of control possible are on the extent of selection of risks permitted, and on the premiums to be charged, but while it may be feasible for such controls to be applied to the home portfolio of a particular class, for example motor vehicle insurance, it is difficult to envisage the operation of such controls internationally in, for example, the marine, aviation and transit class.
An approach to the analysis of claims experience in motor liability excess of loss reinsurance
Authors: Verbeek H. G.
Published: July 2016

In this paper motor liability insurance is considered from the viewpoint of an excess of loss reinsurer.

The reinsurer pays portions of claim amounts in excess of a contractually agreed limit, further referred to as excess point.

Aspects of practical interest are the rating of new contracts and cost-projections on claims occurred in past years which have not yet been reported.

What causes a major difficulty to a rating approach is the timelag between the occurrence of a claim and its settlement.

During this timelag, which may extend to ten years or even longer, the size of a claim will usually increase considerably. This is due to such factors as inflation and more victim oriented legal procedures.

As a result of this phenomenon, a claim, initially not involving the reinsurer, may confront him many years later, when its size overtakes the excess point. Hence, each risk year produces a generation of claims stretching far into the future.

The problem facing the reinsurer trying to compute premiums is that he must look, say ten years into the future, on the basis of incomplete data.

The table below is a schematic presentation of the time history of a contract that started k years ago.

The experience is assumed to be expressed in numbers of claims exceeding a constant excess point.

Successive rows show the generations of excess claims down to the last completed risk year k.

In the pages that follow we will attempt to project expected numbers of excess claims into the future, using information as schematized in this table.
A discipline for the avoidance of unnecessary assumptions
Authors: Roberts Lewis H.
Published: July 2016

Although unnecessary assumptions are something we all try to avoid, advice on how to do so is much harder to come by than admonition. The most widely quoted dictum on the subject, often referred to by writers on philosophy as “Ockham's razor” and attributed generally to William of Ockham, states “Entia non sunt multiplicanda praeter necessitatem”. (Entities are not to be multiplied without necessity.) As pointed out in reference [I], however, the authenticity of this attribution is questionable.

The same reference mentions Newton's essentially similar statement in his Principia Mathematica of 1726. Hume [3] is credited by Tribus [2c] with pointing out in 1740 that the problem of statistical inference is to find an assignment of probabilities that “uses the available information and leaves the mind unbiased with respect to what is not known.” The difficulty is that often our data are incomplete and we do not know how to create an intelligible interpretation without filling in some gaps. Assumptions, like sin, are much more easily condemned than avoided.

In the author's opinion, important results have been achieved in recent years toward solving the problem of how best to utilize data that might heretofore have been regarded as inadequate. The approach taken and the relevance of this work to certain actuarial problems will now be discussed.

Bias and Prejudice

One type of unnecessary assumption lies in the supposition that a given estimator is unbiased when in fact it has a bias. We need not discuss this aspect of our subject at length here since what we might consider the scalar case of the general problem is well covered in textbooks and papers on sampling theory. Suffice it to say that an estimator is said to be biased if its expected value differs by an incalculable degree from the quantity being estimated. Such differences can arise either through faulty procedures of data collection or through use of biased mathematical formulas. It should be realized that biased formulas and procedures are not necessarily improper when their variance, when added to the bias, is sufficiently small as to yield a mean square error lower than the variance of an alternative, unbiased estimator.
Some Inequalities for Stop-Loss Premiums
Authors: Bühlmann H. , Gagliardi B. , Gerber H. U. , Straub E.
Published: July 2016

In this paper any given risk S (a random variable) is assumed to have a (finite or infinite) mean. We enforce this by imposing E[S−] < ∞.

Let then v(t) be a twice differentiate function with

and let z be a constant with o ≤ z ≤ 1.

We define the premium P as follows

or equivalently

Notation: v−(∞) = ∞.

The definitions (1) and (equivalently) (2) are meaningful because of the

Lemma: a) E[v(S − zQ)] exists for all Q∈(− ∞, + ∞).

b) The set{Q∣ − ∞ < Q < + ∞, E[v(S−zQ)]>v((1−z)Q)} is not empty.

Proof: a)

b) Because of a) E[v(S−zQ)] is always finite or equal to + ∞ If v(− ∞) = − ∞ then E[v(S − zQ)] > v((1 − z)Q) is satisfied for sufficiently small Q. The left hand side of the inequality is a nonincreasing continuous function in P (strictly decreasing if z > 0), while the right hand side is a nondecreasing continuous function in Q (strictly increasing if z > 1).

If v(− ∞) = c finite then E[v(S − zQ)] > c

(otherwise S would need to be equal to − ∞ with probability 1) and again E[v(S − zQ)] > v((1 − z)Q) is satisfied for sufficiently small Q.
Architecture decisions in different product classes for complex products
Authors: Jankovic Marija , Eckert Claudia
Published: July 2016

Many of the most fundamental decisions about a product are made during the system architecture design process. However, how system architecture is designed in practice is not well understood. This paper draws on several research studies related to system architecture design to develop a categorization of system architecture design processes to support the adaptation design methodologies and tools to specific situations. The paper reviews different definitions of system architecture and comments on the relevance of the different perspectives taken in the literature on system architecture to different types of system architecture. The research highlights the need for further empirical research on system architecture design processes as well as on tools to support the engineers creating the system architecture.