De Schepper, A.; Teunen, M.; Goovaerts, M. An analytical inversion of a Laplace transform related to annuities certain. (English) Zbl 0796.62092 Insur. Math. Econ. 14, No. 1, 33-37 (1994). 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. Cited in 16 Documents MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics 44A10 Laplace transform 33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\) Keywords:Laplace inversion of a modified Bessel function; annuities certain; stochastic interest rate PDFBibTeX XMLCite \textit{A. De Schepper} et al., Insur. Math. Econ. 14, No. 1, 33--37 (1994; Zbl 0796.62092) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.