An analytical inversion of a Laplace transform related to annuities certain

DOI10.1016/0167-6687(94)00004-2zbMath0796.62092OpenAlexW2022022200MaRDI QIDQ1329411

Marc J. Goovaerts, M. Teunen, Ann De Schepper

Publication date: 4 July 1994

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6687(94)00004-2

zbMATH Keywords

stochastic interest rateannuities certainLaplace inversion of a modified Bessel function

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Laplace transform (44A10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (16)

A recursive scheme for perpetuities with random positive interest rates. Part I. Analytical results ⋮ An analytic expression for the distribution of the generalized Shiryaev-Roberts diffusion. The Fourier spectral expansion approach ⋮ A straightforward analytical calculation of the distribution of an annuity certain with stochastic interest rate ⋮ IBNR reserves under stochastic interest rates ⋮ The present value of a stochastic perpetuity and the gamma distribution ⋮ Bounds for present value functions with stochastic interest rates and stochastic volatility. ⋮ Optimal asset allocation in life annuities: a note. ⋮ The concept of comonotonicity in actuarial science and finance: applications. ⋮ A Note on the Quasi-stationary Distribution of the Shiryaev Martingale on the Positive Half-Line ⋮ Analytic bounds and approximations for annuities and Asian options ⋮ On life insurance reserves in a stochastic mortality and interest rates environment ⋮ Some problems in actuarial finance involving sums of dependent risks ⋮ The GARCH (1,1)-\(M\) model: results for the densities of the variance and the mean ⋮ Martingales, scale functions and stochastic life annuities: A note ⋮ Supermodular ordering and stochastic annuities ⋮ Stochastic Life Annuities

Cites Work

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• Some further results on annuities certain with random interest
• The Laplace transform of annuities certain with exponential time distribution
• Loi de l'indice du lacet Brownien, et distribution de Hartman-Watson
• The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding
• On some exponential functionals of Brownian motion
• Exact Solution of a Time-Dependent Quantal Harmonic Oscillator with a Singular Perturbation

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