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Insurance Risk and Ruin
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    Insurance Risk and Ruin
    • Online ISBN: 9781316650776
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Book description

The focus of this book is on the two major areas of risk theory: aggregate claims distributions and ruin theory. For aggregate claims distributions, detailed descriptions are given of recursive techniques that can be used in the individual and collective risk models. For the collective model, the book discusses different classes of counting distribution, and presents recursion schemes for probability functions and moments. For the individual model, the book illustrates the three most commonly applied techniques. Beyond the classical topics in ruin theory, this new edition features an expanded section covering time of ruin problems, Gerber–Shiu functions, and the application of De Vylder approximations. Suitable for a first course in insurance risk theory and extensively classroom tested, the book is accessible to readers with a solid understanding of basic probability. Numerous worked examples are included and each chapter concludes with exercises for which complete solutions are provided.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

S. Asmussen and H. Albrecher (2010) Ruin Probabilities, 2nd edition. World Scientific Publishing, Singapore.

N. De Pril (1985) Recursions for convolutions of arithmetic distributions. ASTIN Bulletin 15, 135–139.

N. De Pril (1986) On the exact computation of the aggregate claims distribution in the individual life model. ASTIN Bulletin 16, 109–112.

N. De Pril (1989) The aggregate claims distribution in the individual risk model with arbitrary positive claims. ASTIN Bulletin 19, 9–24.

N. De Pril and J. Dhaene (1992) Error bounds for compound Poisson approximations of the individual risk model. ASTIN Bulletin 22, 135–148.

D. C. M. Dickson , A. D. Egídio dos Reis and H.R. Waters (1995) Some stable algorithms in ruin theory and their applications. ASTIN Bulletin 25, 153–175.

D. C. M. Dickson and H.R. Waters (1991) Recursive calculation of survival probabilities. ASTIN Bulletin 21, 199–221.

D. C. M. Dickson and H.R. Waters (1999) Multi-period aggregate loss distributions for a life portfolio. ASTIN Bulletin 29, 295–309.

D. C. M. Dickson and H.R. Waters (2002) The distribution of the time to ruin in the classical risk model. ASTIN Bulletin 32, 299–313.

D. C. M. Dickson and G.E. Willmot (2005) The density of the time to ruin in the classical Poisson risk model. ASTIN Bulletin 35, 45–60.

S. Drekic and G.E. Willmot (2003) On the density and moments of the time to ruin with exponential claims. ASTIN Bulletin 33, 11–21.

H.U. Gerber , M.J. Goovaerts and R. Kaas (1987) On the probability and severity of ruin. ASTIN Bulletin 17, 151–163.

H.U. Gerber and G. Pafumi (1998) Utility functions: From risk theory to finance. North American Actuarial Journal 2, No. 3, 74–100.

H.U. Gerber and E. S. W. Shiu (1998) On the time value of ruin. North American Actuarial Journal 2, No. 1, 48–78.

R.V. Hogg and S.A. Klugman (1984) Loss Distributions. John Wiley, New York.

S. Kuon , A. Reich and L. Reimers (1987) Panjer vs De Pril vs Kornya: A comparison from a practical point of view. ASTIN Bulletin 17, 183–191.

H.H. Panjer (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 21–26.

H.H. Panjer (1986) Direct calculation of ruin probabilities. Journal of Risk and Insurance 53, 521–529.

H.H. Panjer and S. Wang (1993) On the stability of recursive formulas. ASTIN Bulletin 23, 227–258.

N.U. Prabhu (1961) On the ruin problem of collective risk theory. Annals of Mathematical Statistics 32, 757–764.

T. Rolski , H. Schmidli , V. Schmidt and J. Teugels (1999) Stochastic Processes for Insurance and Finance. John Wiley, Chichester.

B. Sundt (1992) On some extensions of Panjer's class of counting distributions. ASTIN Bulletin 22, 61–80.

B. Sundt and W. S. Jewell (1981) Further results on recursive evaluation of compound distributions. ASTIN Bulletin 12, 27–39.


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