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An analytical inversion of a Laplace transform related to annuities certain. (English) Zbl 0796.62092

Summary: The present contribution deals with the Laplace inversion of a modified Bessel function with respect to the index in a straightforward analytical way. This kind of modified Bessel functions appears when annuities certain with a stochastic interest rate are considered, and also when evaluating the value of Asian options.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
44A10 Laplace transform
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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[1] Camiz, P.; Gerardi, A.; Marchioro, C.; Presutti, E.; Scacciatelli, E., Exact solution of a time dependent quantal harmonic oscillator with a singular perturbation, Journal of Mathematical Physics, 12, no. 10, 2040-2043 (1971) · Zbl 0224.35081
[2] De Schepper, A.; Goovaerts, M. J., Some further results on annuities certain with random interest, Insurance: Mathematics and Economics, 11, no. 4, 283-290 (1992) · Zbl 0784.62092
[3] De Schepper, A.; Goovaerts, M. J.; Delbaen, F., The Laplace transform of annuities certain with exponential time distribution, Insurance: Mathematics and Economics, 11, no. 4, 291-294 (1992) · Zbl 0784.62091
[4] Durfresne, D., The distribution of a perpetuity, with applications to risk theory and pension funding, Scandinavian Actuarial Journal, 39-79 (1990)
[5] Gradshteyn, I. S.; Ryzhik, I. M., (Table of Integrals, Series and Products, 496 (1980), Academic Press: Academic Press London), 951-981 · Zbl 0521.33001
[6] Kawazu, K.; Tanaka, H., On the maximum of a diffusion process in a drifted Brownian environment, (Sém. Probas. Sém. Probas, Lecture Notes in Mathematics 1557, XXVII (1993), Springer: Springer Berlin) · Zbl 0791.60071
[7] Yor, M., Loi de l’indice du lacet brownien et distribution de Hartmann-Watson, Zeitschrift für Wahrscheinlichkeitstheorie, 53, 71-95 (1980) · Zbl 0436.60057
[8] Yor, M., On some exponential functionals of Brownian motion, Advances in Applied Probability, 24, 509-531 (1992) · Zbl 0765.60084
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