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Risk Theory

The Stochastic Basis of Insurance

  • Book
  • © 1977

Overview

Authors:
  1. Robert Eric Beard

    1. London, England

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  2. Teivo Pentikäinen

    1. Helsinki, Finland

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  3. Erkki Pesonen

    1. Helsinki, Finland

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Part of the book series: Ettore Majorana International Science Series (EMISS, volume 1)

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Table of contents (13 chapters)

  1. Front Matter

    Pages iii-xvi
    Download chapter PDF

  2. Definitions and Notations

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 1-6

  3. Process with Constant Size of One Claim

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 7-17

  4. Generalized Poisson Distribution

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 18-40

  5. Normal Approximation and Edgeworth Series for F(x)

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 41-51

  6. Applications of the Normal Approximation

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 52-75

  7. The Esscher Approximation

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 76-90

  8. Monte Carlo Method

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 91-97

  9. Other Methods of Calculating the Generalized Poisson Function

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 98-102

  10. Variance as a Measure of Stability

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 103-109

  11. Varying Basic Probabilities

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 110-131

  12. The Ruin Probability During a Finite Time Period

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 132-136

  13. The Ruin Probability During an Infinite Time Period

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 137-159

  14. Application of Risk Theory to Business Planning

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen
    Pages 160-169

  15. Back Matter

    Pages 170-195
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Keywords

About this book

whioh the developments are appropriate in an elementary text book is open to doubt. Fortunately the proceedings of the conference arranged by the Society of Actuaries Research Committee in September 1974 provide an effective review of the ourrent position (Credibility, Theory and Applications, Ed. P. M. Kahn, Academic Press, 1975). It is doubtful if any practical use is now made of the Esscher approximation and the N-P method is much more convenient and of adequate accuracy in most practical work. Thus the first half of Chapter 6 is now largely of historical interest. Chapter 11 dealing with ruin probability during a finite time interval does not give an adequate view of the current importanoe of this topic but the position is fluid because of the considerable effort being expended in the search for practical methods of calcu­ lation. Formulae are, in general, complicated and involve extensive computer based quadratures or simulation techniques. The paper by Seal in the Scandinavian Actuarial Journal (The Numerical Calculation of U(w,t) the Probability of Non-ruin in an Interval (O,t) 1974) gives a recent treatment and a fairly complete list of relevant references. In many countries studies are currently in progress in the develop­ ment of models for business planning where the basic operations involve a stochastic process. Not only are insurance companies interested but in many commercial and industrial firms the needs are significant so that a very large field exists for applications.

Authors and Affiliations

  • London, England

    Robert Eric Beard

  • Helsinki, Finland

    Teivo Pentikäinen, Erkki Pesonen

Bibliographic Information

  • Book Title: Risk Theory

  • Book Subtitle: The Stochastic Basis of Insurance

  • Authors: Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

  • Series Title: Ettore Majorana International Science Series

  • DOI: https://doi.org/10.1007/978-94-009-5781-7

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: R. E. Beard, T. Pentikäinen, E. Pesonen 1977

  • Softcover ISBN: 978-94-009-5783-1Published: 13 November 2013

  • eBook ISBN: 978-94-009-5781-7Published: 09 March 2013

  • Edition Number: 1

  • Number of Pages: XVI, 195

  • Number of Illustrations: 19 b/w illustrations

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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