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Effective Statistical Methods for Group Insurance by Nanak Chand 140 pages; quality trade paperback (softcover); catalogue #03-0137; ISBN 1-55395-774-1; US$19.95, C$29.73, EUR19.40, £13.40 The book provides analytical techniques useful in determining adequate, equitable, and competitive group health premiums.
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About the Book
Given the risk characteristics and the observed claim cost for the experience period, this book describes some ways in which statistical methods can be used in the calculation of net premiums for individual groups having non-identical risk characteristics and credibility generally less than one.
The applications result in unique credibility formulas that take into account the individual characteristics, and are expected to provide adequate, equitable, and competitive premiums. The underlying methods are designed to be consistent with current actuarial practice, though giving attention to occasional need for suitable modifications.
Since stop loss claim costs are a function of the behavior of the tails of their respective distributions, this part of the book assesses such claim cost using well established parametric models, and provides comprehensive tables of the corresponding stop loss premiums.
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About the Author
Nanak Chand has a Ph.D. in mathematical statistics from the University of North Carolina, is a fellow of the Society of Actuaries, a member of the American Academy of Actuaries, and is enrolled to perform actuarial services under the Employee Retirement Income Security Act (ERISA). He has made noteworthy contributions to statistical methodology and applications as a researcher and as a consultant in the academic as well as in public and private sectors including insurance organizations and employee benefit plans. He has published a number of articles and reviews in statistics in professional journals and in the proceedings of various research conferences.
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Excerpts
Foreword
This book contains compact information on techniques needed in
estimating expected claim costs and stop loss premiums in group health
insurance. These include both standard statistical methods based on
probability theory and practical considerations of model formation and
credibility theory applied to group insurance.
The author ( Dr. Nanak Chand) has combined his deep knowledge of the
former, and his long experience in the latter to provide, in a small
compass, a concise presentation of essential principles, together with
adequate examples.
The book requires, and will repay, careful reading and study. The presentation is clear, and every word is relevant.
Norman L. Johnson
Chapell Hill, North Carolina,
December 2002
Introduction
This monograph describes some ways in which statistical methods can
be used in the evaluation of claim costs and related quantities. The
methods are presented as providing useful insights for combination with
standard actuarial techniques. It is to be hoped that such combined
approaches will lead to improved understanding of the problem and
improved estimates of relevant quantities.
The proposed methods utilize a background of probability theory
applied to statistical analysis. This is the topic of Chapter 2, which
contains a condensed summary of the concepts employed, together with
relevant notation. To apply them in specific cases, a model must be
constructed. To obtain useful results, the model must be sufficiently
close to reality, and also reflect current actuarial practice, so some care is
needed in its construction.
Chapter 3 is devoted to consideration of the above problems, with
particular reference to consistency with current practice, though giving
attention to occasional need for suitable modifications, and continues
with a discussion of estimation of parameters in the models, with some
numerical examples.
Chapter 4 describes the incorporation of credibility concepts and
measurements in this work. In Chapter 5, the calculation of expected
stop loss claim cost is described, using three possible families of assumed
mathematical forms - gamma, lognormal, and Weibull. Again, there are
numerical examples of the relevant calculations.
Following some concluding remarks in Chapter 6, there are extensive
tables of hypothetical data for one hundred groups, of the kind needed
for constructing the models of Chapters 3 and 4. In addition, there are
tables of net stop loss premiums for the distributions studied in Chapter5. Chapter 6 also contains a description of the objectives and contents of
these tables, portions of which are used in the numerical examples in the
text.
The claim cost estimation techniques developed in this book are based
on several different sources of material in the literature on mathematical
statistics and actuarial science. The list of references at the conclusion of
the book indicates the chapters to which an entry is related.
However, since the objective is to make this work self-contained, study
of all of this body of literature is not a prerequisite for understanding
and applying the methods of this book. If additional reading is desired,
the classical books [21] and [97] provide a comprehensive account of the
basic concepts of mathematical statistics, including the development of
probability measures and the treatment of multivariate structures.
Chapter 6
Summary and Conclusion
6.1 Basic Issue
Given the risk characteristics and the observed claim cost for the
experience period, the first objective is to estimate the true claim cost for
each of the individual groups in the class, resulting in turn in, adequate,
equitable, and competitive premiums. In this case, we are dealing with
groups of size such that the corresponding observed claim costs are not
statistically reliable. The second objective is to study the behavior of the
tails of the claim cost distributions, thereby assessing the expected stop
loss claim costs for various levels for all size groups.
6.2 Basic Approach
When dealing with groups having non-identical characteristics and
credibility less than one, a suitable approach is to integrate the claim
experience and risk characteristics of the group with those of others in
the class. The method results in a credibility formula and a claim cost
estimate that takes into account the characteristics of the individual
groups. Stop loss claim costs are a function of the behavior of the claim
cost curves in their tails, necessitating the appropriateness of the
estimators of the parameters and that of the assumed parametric models.
6.3 Concluding Remarks
The first four chapters of this monograph contain descriptions of the
elements entering into the assessment of the true claim costs, starting
from the needed initial data, through accounts and rationale for the
methods to be used to the final estimates and their interpretation. Chapter 5 similarly deals with assessment of the expected stop loss claim
costs.
In using this information, it will, of course be necessary to make use of
knowledge of features of the specific case under consideration. There
might, for example, be other risk factors beyond those used in Chapter 3,
and there may be other possible CDF's than those in Chapter 5,
depending on the kind of cost distributions it is felt are likely to be
encountered. Chapters 3 and 5 contain more relevant ideas on these
possibilities.
The reader should also bear in mind that the model of Chapter 3 is not
'graven in stone', it is necessarily based on the user's background
knowledge. Nevertheless, the general methods of approach, as distinct
from specific techniques appropriate in special cases, should be of the
nature described. Indeed, one should be open to the possibility of
changing specific forms of assumptions, either because accumulation of
data provides compelling evidence for such reassessment, or because the
situation itself has changed, or, of course, both.
Catalogue Information
