Effective Statistical Methods for Group Insurance - Softcover

Chand, Nanak

Softcover

ISBN 10: 1553957741 ISBN 13: 9781553957744

Publisher: Trafford Publishing, 2006

Synopsis

The book provides analytical techniques useful in determining adequate, equitable, and competitive group health premiums.

About this title

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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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.

Edition details

• Publisher: Trafford Publishing
• Publication date: 2006
• Language: English
• ISBN 10: 1553957741
• ISBN 13: 9781553957744
• Binding: Paperback
• Number of pages: 144