Calculating multivariate ruin probabilities via Gaver-Stehfest inversion technique

DOI10.1016/S0167-6687(99)00029-3zbMath1028.91561OpenAlexW1990587437MaRDI QIDQ1962823

Miguel A. Usábel

Publication date: 31 January 2000

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

Full work available at URL: https://doi.org/10.1016/s0167-6687(99)00029-3

zbMATH Keywords

Laplace transformnumerical methodsintegral equationsGaver-Stehfest method

Mathematics Subject Classification ID

Related Items (11)

Risk-neutral and actual default probabilities with an endogenous bankruptcy jump-diffusion model ⋮ A solution to the ruin problem for Pareto distributions. ⋮ Unnamed Item ⋮ Practical approximations for multivariate characteristics of risk processes ⋮ On the valuation of constant barrier options under spectrally one-sided exponential Lévy models and Carr's approximation for American puts. ⋮ A numerical method for the expected penalty-reward function in a Markov-modulated jump-diffusion process ⋮ Compliance of the Token-Bucket Model with Markovian Traffic ⋮ Risk processes analyzed as fluid queues ⋮ Ruin probabilities by Padé's method: simple moments based mixed exponential approximations (Renyi, De Vylder, Cramér-Lundberg), and high precision approximations with both light and heavy tails ⋮ Liquidation risk in insurance under contemporary regulatory frameworks ⋮ Evaluation and default time for companies with uncertain cash flows

Cites Work

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• Taylor-series expansion for multivariate characteristics of classical risk processes
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• How to calculate ruin probabilities according to the classical risk theory
• Numerical inversion of characteristic functions
• Ruin probabilities prepared for numerical calculation
• Algorithm 719: Multiprecision translation and execution of FORTRAN programs
• A Fortran 90-based multiprecision system
• Fourier inversion—distribution functions—long tails
• The numerical calculation ofU(w, t), the probability of non-ruin in an interval (0,t)
• Numerical Inversion of Laplace Transforms Using Laguerre Functions
• New quadrature formulas for the numerical inversion of the Laplace transform

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