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1963
In the discussion in the ASTIN Colloquium 1962, which followed my lecture on the numerical evaluation of the distribution functions defining some compound Poisson processes, a remark was made, which drew my attention to the paper quoted here below under reference number (I), On composed Poisson distributions I.
1963
In this paper, deceptively simple in concept though perhaps not simple in mathematical detail, Mr. Carlson has accomplished three things, one of which possibly exceeds the limits of his own original objectives. First, the paper constitutes an excellent historical summary of various approaches to the negative binomial distribution in general, including presentation of one such approach in some detail.
1963
Mr. Carlson sets forth one of the reasons for writing his paper in these words: "... We are all interested in finding tools that work. But we should not be satisfied as actuaries without probing into any unfamiliar mathematical model until we know why it works, because thus only do we learn whether it is the best model for the purpose or whether is can be improved upon, and also what extensions of its utility may be available ....
1963
Mr. Bailey has again contributed significantly to our Proceedings with the ideas presented in this paper. The ratemaking technique suggested is designed to utilize to the fullest the predictability inherent in the data of each subdivision created by a multiple classification system. Mr. Bailey accomplishes this maximum utilization by producing all sets of adjustments, or relativities, simultaneously.
1963
Mr. Bailey's latest paper is, indeed, a timely contribution to the proceedings of our Society. Timely, not only because it provides a method of calculating rates with minimum bias, but also because it provides ideal computer application. Without the aid of a computer the method is, in fact, impractical.
1963
The paper presents specific methods for obtaining insurance rates that are as accurate as possible for each class and territory and so on. Many of the techniques presented in the paper are already in use by the various bureaus and other ratemakers in one form or another.
1963
Risk Theory for Life Insurance is simplified by the fact that the distribution ? (x) of claim amounts x approximately coincide with the distribution of "Risk sums" (not exactly, owing to differences in the claim frequency with age and actual state of health).
1963
The compound Poisson process in the wide sense is defined as a process for which the probability distribution of the number i of changes in the random function attached to the process, while the parameter passes from o to a fixed value x of the parameter measured on a suitable scale, is given by the Laplace-Stieltjes integral (variable) where U(v, x) for a fixed value of x defines the distribution of v.
1963
The estimation of stop loss premiums can be based on some knowledge about the distribution function of the sum of all claims in a year (assuming that the stop loss insurance relates to a period of one calendar year). Generally speaking there are two methods to obtain this knowledge about the distribution function.
LOB-Fire and Allied Lines/Reinsurance
1963
One of the most difficult tasks facing the Group Actuary today is the development of proper rates for Comprehensive Medical Insurance. The newness of the coverage, the variety of benefit provisions offered, and the many variables which affect the cost o£ this product have combined to raise numerous questions as to what statistical data should be assembled and how it should be analyzed for the purposes of ratemaking. The fact that Mr.
1963
Mr. Bevan has presented a paper on a subject where it is unlikely that we will ever be surfeited with data. Every study of comprehensive medical insurance reveals some new fact, sometimes difficult to reconcile with previous experience. The ratemaking problem is thus a matter of grappling with these disparities using as many sources of information as are available to the actuary. Mr. Bevan's contribution is a significant addition to our sources.
1963
In their original form, Accident and Health policies typically extended coverage on the basis of stipulated benefits for hospital, surgical and medical expenses. About 15 years ago, however, the concept of Major Medical coverage began to emerge, which concept tended to cut across benefit maximums by type of medical expense and imposed only maximums of $5,000 or $10,000 for all expenses combined arising out of one disability.
1963
Commercial multiple peril package policies have been in existence since 1958 and at this time are still new enough so that they have not yet really passed beyond the evolutionary or seasoning stage.
1963
This actuarial note under discussion "Fixed and Variable Expenses" has as its closing remark a little philosophy which we are all aware of, but many times it is forgotten. Mr. Lewis Roberts suggests that "... we take pains to be sure that the sense in which the word is used is clear .... " Also, that more descriptive terms be used instead of a general word "...
1963
As one who is constantly being tripped up by terminology I find Mr. Roberts' paper on Fixed and Variable Expenses extremely helpful. It should be required reading for those of us who are faced with the forthcoming study of expenses by size of risk for Workmen's Compensation on Liability lines. Such a study after all concerns itself with an analysis of "fixed expenses" which include those defined by Mr. Roberts as " ' ...
1963
A variety of meanings appear to have been attached to the expression "fixed expenses," with the result that we sometimes find ourselves talking at cross-purposes. The intent of this note is to see if any clarification is possible. A cost which does not depend upon a particular variable is by definition constant, or fixed, with respect to that variable.
1962
The most important property of a distribution function to be used as a model for the distribution of one claim is of course that it fits the data well enough. If there is no natural truncation point in the data a more formal demand is that all the moments of the distribution function exist. Further, to be of a real value to the statistician, the chosen d.f. ought to be reasonably handy to use. As all the moments of the lognormal d.f.
1962
When the All-Industry Bills were adopted in 1946, Multi-Peril Package Policies, particularly the Homeowners Policy, had not been conceived. It is understandable, therefore, that certain phraseology of the All-Industry Bills was not readily adaptable to changing conditions and philosophies which were subsequently dictated by the introduction of package policies.
1962
The problem of dwelling policies written for small amounts is one with which many in the property insurance field have long been concerned. Originally attention was centered on insurance to value as shown by a 1952 statement that "...
1962
The reader should have very little difficulty with Mr. Buffinton's interesting paper on "The Low Valued Risk." Its purpose is indicated by the subtitle, "A Study of the Premium Required for Habitational Risks of Various Policy Amounts." Within the specified framework, the reviewer found himself often in accord with the author's observations. There were, however, some phases of the argument on which we should like to comment.
1962
A previous paper l generated a number of comments and requests that expenses by company size of premium volume for each 15ne of business be analyzed for lines of business such as fire, extended coverage, multiple peril, etc. Accordingly, calendar year 1961 expenses for almost every line. of business have been reviewed and summarized for stock insurance companies as will be set forth later.
1962
The bonus system used by Finnish insurers is as follows: Policies are divided into 4 bonus classes, C1, C2, C8, C4, each of them being initially placed in class C 1. After one clairnless year, a policy placed in class Ch is transferred to class C h ÷ 1 (h _ 3) from the beginning of the following year.
1962
This paper provides background for the classical credibility formulas that are still in use today. This paper should not be ignored by advocates of more "up to date" credibility. Its verbal description of how credibility formulas should be used would do a Bayesian proud.
1962
The description, interpretation, and curve fitting of the negative binomial distribution has become a topic of great interest to American actuaries in the last few years. What is it? Where did it come from? What does it mean? How can it be used? These and many other questions have been asked by all of us. The first thing to do, of course, is to check the textbooks and references in our personal libraries.
