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  1. Home
  2. Books
  3. Insurance Risk and Ruin
  • Cited by 28
Publisher:
Cambridge University Press
Online publication date:
November 2016
Print publication year:
2016
Online ISBN:
9781316650776
DOI:
https://doi.org/10.1017/9781316650776
Subjects:
Economics, Statistics for Econometrics, Finance and Insurance, Finance and Accountancy, General Statistics and Probability, Statistics and Probability
Series:
International Series on Actuarial Science
Information

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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Contents

Contents
References
References
Albrecher, H. and Boxma, O. (2005) On the discounted penalty function in a Markovdependent risk model. Insurance: Mathematics & Economics 37, 650–672.
Asmussen, S. and Albrecher, H. (2010) Ruin Probabilities, 2nd edition. World Scientific Publishing, Singapore.
Borch, K. (1990) Economics of Insurance. North-Holland, Amsterdam.
Bühlmann, H. (1980) An economic premium principle. ASTIN Bulletin 11, 52–60.
Centeno, M.L. (1986) Measuring the effects of reinsurance by the adjustment coefficient. Insurance: Mathematics & Economics 5, 169–182.
De Pril, N. (1985) Recursions for convolutions of arithmetic distributions. ASTIN Bulletin 15, 135–139.
De Pril, N. (1986) On the exact computation of the aggregate claims distribution in the individual life model. ASTIN Bulletin 16, 109–112.
De Pril, N. (1988) Improved approximations for the aggregate claims distribution of a life insurance portfolio. Scandinavian Actuarial Journal, 61–68.
De Pril, N. (1989) The aggregate claims distribution in the individual risk model with arbitrary positive claims. ASTIN Bulletin 19, 9–24.
De Pril, N. and Dhaene, J. (1992) Error bounds for compound Poisson approximations of the individual risk model. ASTIN Bulletin 22, 135–148.
De Vylder, F. (1978) A practical solution to the problem of ultimate ruin probability. Scandinavian Actuarial Journal, 114–119.
De Vylder, F. and Goovaerts, M.J. (1988) Recursive calculation of finite time survival probabilities. Insurance: Mathematics & Economics 7, 1–8.
Dickson, D. C. M. (1992) On the distribution of the surplus prior to ruin. Insurance: Mathematics & Economics 11, 191–207.
Dickson, D. C. M., Egídio dos Reis, A. D. and Waters, H.R. (1995) Some stable algorithms in ruin theory and their applications. ASTIN Bulletin 25, 153–175.
Dickson, D. C. M., Hughes, B.D. and Zhang, L. (2005) The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims. Scandinavian Actuarial Journal, 358–376.
Dickson, D. C. M. and Li, S. (2010) Finite time ruin problems for the Erlang(2) risk model. Insurance: Mathematics & Economics 46, 12–18.
Dickson, D. C. M. and Waters, H.R. (1991) Recursive calculation of survival probabilities. ASTIN Bulletin 21, 199–221.
Dickson, D. C. M. and Waters, H.R. (1996) Reinsurance and ruin. Insurance: Mathematics & Economics 19, 61–80.
Dickson, D. C. M. and Waters, H.R. (1999) Multi-period aggregate loss distributions for a life portfolio. ASTIN Bulletin 29, 295–309.
Dickson, D. C. M. and Waters, H.R. (2002) The distribution of the time to ruin in the classical risk model. ASTIN Bulletin 32, 299–313.
Dickson, D. C. M. and Waters, H.R. (2004) Some optimal dividends problems. ASTIN Bulletin 34, 49–74.
Dickson, D. C. M. and Willmot, G.E. (2005) The density of the time to ruin in the classical Poisson risk model. ASTIN Bulletin 35, 45–60.
Drekic, S. and Willmot, G.E. (2003) On the density and moments of the time to ruin with exponential claims. ASTIN Bulletin 33, 11–21.
Dufresne, F. and Gerber, H.U. (1989) Three methods to calculate the probability of ruin. ASTIN Bulletin 19, 71–90.
Feller, W. (1966) An Introduction to Probability Theory and Its Applications, Volume 2. Wiley, New York.
Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. S. S. Huebner Foundation, Philadelphia, PA.
Gerber, H.U., Goovaerts, M.J. and Kaas, R. (1987) On the probability and severity of ruin. ASTIN Bulletin 17, 151–163.
Gerber, H.U. and Pafumi, G. (1998) Utility functions: From risk theory to finance. North American Actuarial Journal 2, No. 3, 74–100.
Gerber, H.U. and Shiu, E. S. W. (1998) On the time value of ruin. North American Actuarial Journal 2, No. 1, 48–78.
Goovaerts, M.J., De Vylder, F. and Haezendonck, J. (1984) Insurance premiums. North-Holland, Amsterdam.
Grimmett, G.R. and Welsh, D.J.A. (1986) Probability: An Introduction. Oxford University Press, Oxford.
Hogg, R.V. and Klugman, S.A. (1984) Loss Distributions. John Wiley, New York.
Klugman, S.A., Panjer, H.H. and Willmot, G.E. (1998) Loss Models – From Data to Decisions. John Wiley, New York.
Kornya, P.S. (1983) Distribution of aggregate claims in the individual risk theory model (with discussion). Transactions of the Society of Actuaries 35, 823–858.
Kuon, S., Reich, A. and Reimers, L. (1987) Panjer vs De Pril vs Kornya: A comparison from a practical point of view. ASTIN Bulletin 17, 183–191.
Lin, X.S. and Pavlova, K. (2006). The compound Poisson risk model with a threshold dividend strategy. Insurance: Mathematics & Economics 38, 57–80.
Lin, X.S. and Willmot, G.E. (2000) The moments of the time of ruin, the surplus before ruin, and the deficit at ruin. Insurance: Mathematics & Economics 27, 19–44.
Panjer, H.H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 21–26.
Panjer, H.H. (1986) Direct calculation of ruin probabilities. Journal of Risk and Insurance 53, 521–529.
Panjer, H.H. and Lutek, B.W. (1983) Practical aspects of stop-loss calculations. Insurance: Mathematics & Economics 2, 159–177.
Panjer, H.H. and Wang, S. (1993) On the stability of recursive formulas. ASTIN Bulletin 23, 227–258.
Panjer, H.H. and Willmot, G.E. (1986) Computational aspects of recursive evaluation of compound distributions. Insurance: Mathematics & Economics 5, 113–116.
Panjer, H.H. and Willmot, G.E. (1992) Insurance Risk Models. Society of Actuaries, Schaumburg, IL.
Picard, P. (1994) On some measures of the severity of ruin in the classical Poisson model. Insurance: Mathematics & Economics 14, 107–115.
Prabhu, N.U. (1961) On the ruin problem of collective risk theory. Annals of Mathematical Statistics 32, 757–764.
Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1999) Stochastic Processes for Insurance and Finance. John Wiley, Chichester.
Schröter, K. J. (1991) On a family of counting distributions and recursions for related compound distributions. Scandinavian Actuarial Journal, 161–175.
Sundt, B. (1992) On some extensions of Panjer's class of counting distributions. ASTIN Bulletin 22, 61–80.
Sundt, B. and Jewell, W. S. (1981) Further results on recursive evaluation of compound distributions. ASTIN Bulletin 12, 27–39.
Wang, S. (1995) Insurance pricing and increased limits ratemaking by proportional hazards transforms. Insurance: Mathematics & Economics 17, 43–54.
Waters, H.R. (1983) Some mathematical aspects of reinsurance. Insurance: Mathematics & Economics 2, 17–26.
Willmot, G.E. and Lin, X.S. (1998) Exact and approximate properties of the distribution of the surplus before and after ruin. Insurance: Mathematics & Economics 23, 91–110.

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