- Email: [email protected]
Harald Cramér and insurance mathematics
234 theory, random walk, test functions, ladder height.
Abstracts and Reviews ruin probability,
c.~~ _ 074022 (Mll) Exact calculation of the aggregate claims distribution in the individual life model by use of an n-layer model. Waldmann K.-H., Blatter der Deutschen Gesellschaft j?ir Versicherungsmathematik, Vol. 22, nr. 2, 1995, pp. 2 79-287. A recursive procedure is suggested for calculating the aggregate claims distribution (stop-loss premium) in the individual life model. The method which is based on the well-known De Pril algorithm results in both a considerably reduction of the number of arithmetic operations to be carried out and the number of data to be kept at each step of iteration. The problem of underflow/overflow which may arise in case of a large number of policies is avoided by iterating in different layers and by suitably defining the transitions between adjacent layers. Thus the algorithm can be applied to a portfolio with an arbitrary number of policies. Keywords: individual life model, aggregate claims distribution, stop-loss premium.
M12: MODELLING OF PORTFOLIOS AND COLLECTIVES 074023 (M12) The effects of quantized data. Jewel1 W.S., University of California, Berkeley, Applied Stochastic Models and Data Analysis, Vol. II, nr. 3, 1995, pp. 201-216. The effects of quantized data upon parameter estimation are investigated by re-.examining a variety of simple and complicated risk models previously studied by the author. In spite of this unifying theme, no general principles arise, except for demonstrating that estimation in models with two or more parameters can lead to unpredictable results, with or without the introduction to discrete data. In fact, certain common actuarial models are shown always to have poor estimation properties, even using substantial amounts of continuous data. The paper concludes with a plea for the redevelopment of classical models that are continuous in nature, rather than perpetuating the current discrete multi-parameter models, whose estimation properties are poor, since modern technology now permits inexpensive capture of
all kinds of continuous data. Keywords: quantized data, risk models. M13: RUIN AND OTHER STABILITY CRITERIA 074024 (M13) Harald Cramer and Insurance Mathematics. Martin-LSf A., Stockholm University, Applied Stochastic Models and Data Analysis, Volume I I, nr. 3, 1995, pp. 271-276. A short history of the works of Harald Cramer in insurance mathematics is given. In particular, the early development of the collective risk theory starting with the works of F. Lundberg is outlined. Also, the so called zero point method for premium calculations invented by Cramer is described. Keywords: mathematics in insurance, risk theory, ruin probabilities, safe premium calculations. 074025 (M13) Delay in claim settlement and ruin probability approximations. Kliippelberg C., Mikosch T., Johannes Gutenberg University, Germany, Scandinavian Actuarial Journal, nr. 2, 1995, pp. 154-168. The authors introduce a general risk model for portfolios with delayed claims which is a natural extension of the classical Poisson model. They investigate ruin problems for different premium principles and provide approximations for the ruin probability: They conclude with some specific models, for example, for IBNR portfolios and portfolios where the pay-off process depends on the claim size. Keywords: IBNR claims, risk reserves, ruin probability, shot-noise process. 074026 (M13) Saddlepoint approximations for the probability of ruin in finite time. Barndorff-Nielsen O.E., Schmidli H., University of’ Aarhus, Denmark, Scandinavian Actuarial Journal, nr. 2, 1995, pp. 169-186. Saddlepoint techniques are applied to obtain approximations for the probability of ruin both in finite and in infinite time for the classical Cramer-Lundberg model. The resulting approximations are compared to exact values. Keywords: Ruin probability, saddlepoint techniques, Laplace transform, cumulantfunction, Cramer-Lundberg
Abstracts and Reviews ruin probability,
c.~~ _ 074022 (Mll) Exact calculation of the aggregate claims distribution in the individual life model by use of an n-layer model. Waldmann K.-H., Blatter der Deutschen Gesellschaft j?ir Versicherungsmathematik, Vol. 22, nr. 2, 1995, pp. 2 79-287. A recursive procedure is suggested for calculating the aggregate claims distribution (stop-loss premium) in the individual life model. The method which is based on the well-known De Pril algorithm results in both a considerably reduction of the number of arithmetic operations to be carried out and the number of data to be kept at each step of iteration. The problem of underflow/overflow which may arise in case of a large number of policies is avoided by iterating in different layers and by suitably defining the transitions between adjacent layers. Thus the algorithm can be applied to a portfolio with an arbitrary number of policies. Keywords: individual life model, aggregate claims distribution, stop-loss premium.
M12: MODELLING OF PORTFOLIOS AND COLLECTIVES 074023 (M12) The effects of quantized data. Jewel1 W.S., University of California, Berkeley, Applied Stochastic Models and Data Analysis, Vol. II, nr. 3, 1995, pp. 201-216. The effects of quantized data upon parameter estimation are investigated by re-.examining a variety of simple and complicated risk models previously studied by the author. In spite of this unifying theme, no general principles arise, except for demonstrating that estimation in models with two or more parameters can lead to unpredictable results, with or without the introduction to discrete data. In fact, certain common actuarial models are shown always to have poor estimation properties, even using substantial amounts of continuous data. The paper concludes with a plea for the redevelopment of classical models that are continuous in nature, rather than perpetuating the current discrete multi-parameter models, whose estimation properties are poor, since modern technology now permits inexpensive capture of
all kinds of continuous data. Keywords: quantized data, risk models. M13: RUIN AND OTHER STABILITY CRITERIA 074024 (M13) Harald Cramer and Insurance Mathematics. Martin-LSf A., Stockholm University, Applied Stochastic Models and Data Analysis, Volume I I, nr. 3, 1995, pp. 271-276. A short history of the works of Harald Cramer in insurance mathematics is given. In particular, the early development of the collective risk theory starting with the works of F. Lundberg is outlined. Also, the so called zero point method for premium calculations invented by Cramer is described. Keywords: mathematics in insurance, risk theory, ruin probabilities, safe premium calculations. 074025 (M13) Delay in claim settlement and ruin probability approximations. Kliippelberg C., Mikosch T., Johannes Gutenberg University, Germany, Scandinavian Actuarial Journal, nr. 2, 1995, pp. 154-168. The authors introduce a general risk model for portfolios with delayed claims which is a natural extension of the classical Poisson model. They investigate ruin problems for different premium principles and provide approximations for the ruin probability: They conclude with some specific models, for example, for IBNR portfolios and portfolios where the pay-off process depends on the claim size. Keywords: IBNR claims, risk reserves, ruin probability, shot-noise process. 074026 (M13) Saddlepoint approximations for the probability of ruin in finite time. Barndorff-Nielsen O.E., Schmidli H., University of’ Aarhus, Denmark, Scandinavian Actuarial Journal, nr. 2, 1995, pp. 169-186. Saddlepoint techniques are applied to obtain approximations for the probability of ruin both in finite and in infinite time for the classical Cramer-Lundberg model. The resulting approximations are compared to exact values. Keywords: Ruin probability, saddlepoint techniques, Laplace transform, cumulantfunction, Cramer-Lundberg