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Applications of Gaver-Stehfest method of inverting laplace transforms to ruin theory

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1997
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Facultad de Ciencias Económicas y Empresariales. Decanato
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Abstract
The Stehfest-Gaver method of inverting Laplace transforms is a very useful tool in approximating non-ruin probabilities. An accuracy of 6 to 10 significant digits is obtained in every case studied (Tables 1,2 and 3) except for Log-normal claim size and large initial reserves where the accuracy of the "exact" values (using Product integration ) is not guaranteed to be more than 5 digits. The efficiency in terms of computational time is also outstanding because we onIy need to evaluate 20 times the Laplace transform of the c.dJ. of the claim size as shown in (1.6).
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UCM subjects
Probabilidades (Matemáticas) , Teoría de la decisión
Unesco subjects
1209.04 Teoría y Proceso de decisión
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Citation
Bühlmann, H. (1970). Mathematical methods in Risk Theory. Springer-Verlag, New York. Burden, R. L. and Faires, J. D (1985). Numerical Analysis, P.W.S., Boston. Davies,B and Martin,B. (1979). Numerical inversion of the Laplace transform: a survey and comparison of methods. Journal of computational physics,33. Delves, L. M. and Mohamed, J. L. (1985). Computational methods for integral equations. Cambridge, England. Cambridge University Press. Feller, W. (1973). An introduction to probability and its applications. Volume II John Willey. Gaver, D. P. (1966). Operational Research. 14,444-459. Grandell, J. (1990). Aspects of Risk Theory. Springer-Verlag. New York. Haber, S. (1970). Numerical evaluation of multiple integrals, SIAM Rev., 12, 481-526. Panjer, R.H. (1981). Recursive evaluation of a family of compound distributions, ASTIN Bulletin, 12, 22-26. Panjer, R.H. & Willmot, G.E. (1992). Insurance risk Models, Society of Actuaries, Schaumburg. Ramsay, C.M. (1992a). "A Practical Algorithm for Approximating the Probability of Ruin." Transactions of the Society of Actuaries, XLIV, 443-59. Ramsay, C.M. (1992b). "Improving Goovaerts' and De Vylder's Stable Recursive AIgorithm. ASTIN Bulletin, 22, 51-59. Ramsay,C.M. and Usábel,M.A. (1997).Calculating Ruin probabilities via Product integration. Próxima aparición ASTIN BULLETIN Noviembre 1997. cv Stehfest, R. (1970). Numerical inversion of Laplace transform. Communications of the ACM, Vol. 19. No 1.
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https://hdl.handle.net/20.500.14352/64126
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