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083008 (M10, M52) Best bounds for expected financial payoffs II: Applications
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Abstracts and Reviews
083004 (M02) Permanent Disability Of Impaired Assured Lives. Deis A., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 487-496. In Denmark impaired lives are rated according to a system of excess mortality and disability tables. This paper gives results from an analysis of permanent disability for the population of impaired lives assessed and registered in the period 1985-91, based on public register data. Keywords: Permanent disability.
approximative computation of their distributions and related quantities can be done in the mathematical framework of generalized pseudo compound Poisson distributions, which are characterized by integral equations of Volterra type. The results by Dhaene and De Pril (1994) are extended to this more general class of models. The method is illustrated at a mean scaled individual risk model. Keywords: Mean scaling, Aggregate claims, Portfolio models, Gamma distribution, Pseudo compound poisson distribution, Integral equation, Continuous approximation.
MIO: PROBABILITY THEORY AND MATHE-
083007 (M10, M52) Best Bounds For Expected Financial Payoffs I: Algorithmic Evaluation. Hiirlimann W., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 584 - 598. A systematic approach to the evaluation of best bounds for expected financial payoffs, in case the mean, variance and range of the distribution are known, is presented. It is based on the majorant/minorant mathematical technique, which consists to bound a payoff by some quadratic polynomial. For the class of piecewise linear payoff functions, a classification of the global triatomic extrema is given, and a general algorithm for evaluation is formulated. Keywords: Best bounds, Triatomic risks, Piecewise finear, Algorithm, Reinsurance, Derivatives.
MATICAL STATISTICS IN INSURANCE, GENERAL AND MISCELLANEOUS
083005 (M10, Mll) On Mean Scaled Compound Distributions. Hiirlimann W., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 552 - 564. A characterizing problem for scale compound parametric families of distributions with the mean as scale parameter is analyzed. If the counting distribution of the compound family has the sample mean as maximum likelihood estimator of the counting mean, and if the maximum likelihood estimator of the mean scale parameter is the sample mean, then the compound family has necessarily a gamma secondary distribution. Necessary and sufficient conditions under which such a characterization holds are derived. Among the rich class of counting statistical models, which lead to such a characterization, one finds the Poisson, binomial, negative binomial, Hermite, Delaporte, extended Poisson-Pascal, mixed Poisson inverse Gaussian, Sichel, generalized Euler, and many others. The mixed Poisson lognormal is a counterexample for which the present characterization fails. Keywords : Compound distribution, Scale family, Sample mean maximum likelihood property, Orthogonal parameters, Gamma distribution. 083006 (M10, MI1) A Mean Scaled Individual Risk Model And Its Approximative Computation. Hiirlimann W., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 565 - 584. Building on a new theory of statistical risk models initiated in Hilrlimann (1995a/95b), it is shown how mean scaled portfolio models can be constructed. The
083008 (M10, M52) Best Bounds For Expected Financial Payoffs II: Applications. Hiirlimann W,, XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 1, pp. 599 - 613. Based on a general algorithm to determine best bounds for expected piecewise linear payoffs, several important examples are treated in an unified manner. Tables of best bounds are given for the stop-loss, limited stop-loss, franchise and disappearing deductible, and two-layers stop-loss contracts. In the last example the maximal bound can only be obtained numerically. Keywords: Best bounds, Triatomic risks, Piecewise linear, Algorithm, Reinsurance, Derivatives. 083009 (M10, El0) An Elementary Unified Approach To Some Loss Variance Bounds. Hiirlimann W., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 614 - 625.
Abstracts and Reviews
083004 (M02) Permanent Disability Of Impaired Assured Lives. Deis A., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 487-496. In Denmark impaired lives are rated according to a system of excess mortality and disability tables. This paper gives results from an analysis of permanent disability for the population of impaired lives assessed and registered in the period 1985-91, based on public register data. Keywords: Permanent disability.
approximative computation of their distributions and related quantities can be done in the mathematical framework of generalized pseudo compound Poisson distributions, which are characterized by integral equations of Volterra type. The results by Dhaene and De Pril (1994) are extended to this more general class of models. The method is illustrated at a mean scaled individual risk model. Keywords: Mean scaling, Aggregate claims, Portfolio models, Gamma distribution, Pseudo compound poisson distribution, Integral equation, Continuous approximation.
MIO: PROBABILITY THEORY AND MATHE-
083007 (M10, M52) Best Bounds For Expected Financial Payoffs I: Algorithmic Evaluation. Hiirlimann W., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 584 - 598. A systematic approach to the evaluation of best bounds for expected financial payoffs, in case the mean, variance and range of the distribution are known, is presented. It is based on the majorant/minorant mathematical technique, which consists to bound a payoff by some quadratic polynomial. For the class of piecewise linear payoff functions, a classification of the global triatomic extrema is given, and a general algorithm for evaluation is formulated. Keywords: Best bounds, Triatomic risks, Piecewise finear, Algorithm, Reinsurance, Derivatives.
MATICAL STATISTICS IN INSURANCE, GENERAL AND MISCELLANEOUS
083005 (M10, Mll) On Mean Scaled Compound Distributions. Hiirlimann W., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 552 - 564. A characterizing problem for scale compound parametric families of distributions with the mean as scale parameter is analyzed. If the counting distribution of the compound family has the sample mean as maximum likelihood estimator of the counting mean, and if the maximum likelihood estimator of the mean scale parameter is the sample mean, then the compound family has necessarily a gamma secondary distribution. Necessary and sufficient conditions under which such a characterization holds are derived. Among the rich class of counting statistical models, which lead to such a characterization, one finds the Poisson, binomial, negative binomial, Hermite, Delaporte, extended Poisson-Pascal, mixed Poisson inverse Gaussian, Sichel, generalized Euler, and many others. The mixed Poisson lognormal is a counterexample for which the present characterization fails. Keywords : Compound distribution, Scale family, Sample mean maximum likelihood property, Orthogonal parameters, Gamma distribution. 083006 (M10, MI1) A Mean Scaled Individual Risk Model And Its Approximative Computation. Hiirlimann W., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 565 - 584. Building on a new theory of statistical risk models initiated in Hilrlimann (1995a/95b), it is shown how mean scaled portfolio models can be constructed. The
083008 (M10, M52) Best Bounds For Expected Financial Payoffs II: Applications. Hiirlimann W,, XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 1, pp. 599 - 613. Based on a general algorithm to determine best bounds for expected piecewise linear payoffs, several important examples are treated in an unified manner. Tables of best bounds are given for the stop-loss, limited stop-loss, franchise and disappearing deductible, and two-layers stop-loss contracts. In the last example the maximal bound can only be obtained numerically. Keywords: Best bounds, Triatomic risks, Piecewise linear, Algorithm, Reinsurance, Derivatives. 083009 (M10, El0) An Elementary Unified Approach To Some Loss Variance Bounds. Hiirlimann W., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, Volume 2, pp. 614 - 625.