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- W805708812 abstract "Levy processes (LP) are gaining popularity in actuarial and financial modeling. The Levy measure is a key factor in the versatility of LP applications. The estimation of the Levy measure from data is shown to be useful in analyzing the aggregate claims processes in Risk Theory. Starting with infinitely divisible distributions (IDD), some nice constructions are obtained for finite sums of Levy processes. The Levy properties of compound Poisson processes are extensively used in the thesis. Examples illustrate the close relationship between IDDs and Levy processes. The Poisson random measure associated with jumps of a Levy process exceeding a given threshold is discussed and a new derivation is obtained. The relation with subordinators (increasing Levy processes) is explored. Intuitive ideas and results are obtained for the jump function G appearing in Levy's characterization of the Levy-Khinchine formula. A non-parametric estimator of G is discussed. A detailed relation between G and p, the Levy measure, is derived, yielding an estimator of p. The latter gives an estimator of the Poisson rate n f and the claim size distribution F f for claims larger than the threshold f. Extensive numerical simulations illustrate the paths of gamma, inverse Gaussian and {460}-stable claim subordinators and their corresponding estimates for n f and F f" @default.
- W805708812 created "2016-06-24" @default.
- W805708812 creator A5000960472 @default.
- W805708812 date "2007-01-01" @default.
- W805708812 modified "2023-09-27" @default.
- W805708812 title "Estimation of the Lévy measure for the aggregate claims process in risk theory" @default.
- W805708812 hasPublicationYear "2007" @default.
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