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Comparing Risks

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Actuarial Science

Part of the book series: The University of Western Ontario Series in Philosophy of Science ((WONS,volume 39))

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Abstract

In this paper we consider the problem of comparing probability distributions by their degree of risk. We survey one method of making such a comparison and discuss various actuarial applications. Generalizations and simplified proofs of some of the known mathematical results are given. A somewhat similar theme was considered by Goovaerts et al. (1982), but for the most part our applications and methods are different.

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References

  • Arrow, K. J. (1963), “Uncertainty and the welfare economics of medical care.”. American Economic Review 53, 941–973.

    Google Scholar 

  • Bowers, N. L., H. U. Gerber, J. C. Hickman, D. A. Jones, and C. J. Nesbitt (1982), Actuarial Mathematics, Society of Actuaries.

    Google Scholar 

  • Chong, K. (1974), “Some extensions of a theorem of Hardy, Littlewood, and Pólya and their applications.”. Canadian Journal of Mathematics 26, 1321–1340.

    Article  MathSciNet  MATH  Google Scholar 

  • Goovaerts, M. J., F. De Vylder, and J. Haezendonck (1982), “Ordering of risks: a review.”. Insurance: Mathematics and Economics 1, 131–161.

    Article  MathSciNet  MATH  Google Scholar 

  • Goovaerts, M. J., and F. De Vylder (1983), “Upper and lower bounds on infinite time ruin probabilities in case of constraint on claim size distributions.”. Journal of Econometrics 23, 77–90.

    Article  MathSciNet  MATH  Google Scholar 

  • Hardy, G. H., J. E. Littlewood, and G. Pólya (1929), “Some simple inequalities satisfied by convex functions.”. Messenger of Mathematics 58, 145–152.

    Google Scholar 

  • Hardy, G. H., J. E. Littlewood, and G. Pólya (1952), Inequalities. London: Cambridge University Press.

    MATH  Google Scholar 

  • Marshall, A. W., and I. Olkin (1979), Inequalities; Theory of Majorization and its Applications. New York: Academic Press.

    MATH  Google Scholar 

  • Rothschild, M., and J. E. Stiglitz (1970), “Increasing risk, 1: A definition.”. Journal of Economic Theory 2, 225–243.

    Article  MathSciNet  Google Scholar 

  • Stoyan, D. (1983), Comparison Methods for Queues and Other Stochastic Models. New York: Wiley and Sons.

    MATH  Google Scholar 

  • Strassen, V. (1965), “The existence of probability measures with given marginals.”. Annals of Mathematical Statistics 36, 423–429.

    Article  MathSciNet  MATH  Google Scholar 

  • Whitt, W. (1980), “The effect of variability in the Gl/G/s queue.”. Journal of Applied Probability 17, 1062–1071.

    Article  MathSciNet  MATH  Google Scholar 

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© 1987 D. Reidel Publishing Company, Dordrecht, Holland

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Promislow, S.D. (1987). Comparing Risks. In: MacNeill, I.B., Umphrey, G.J., Chan, B.S.C., Provost, S.B. (eds) Actuarial Science. The University of Western Ontario Series in Philosophy of Science, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4796-2_6

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  • DOI: https://doi.org/10.1007/978-94-009-4796-2_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8627-1

  • Online ISBN: 978-94-009-4796-2

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