Saddlepoint approximations to the probability of ruin in finite time for the compound Poisson risk process perturbed by diffusion

DOI10.1007/S11009-014-9412-9zbMath1336.60052OpenAlexW2020198323MaRDI QIDQ267897

Benjamin Baumgartner, Riccardo Gatto

Publication date: 12 April 2016

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://boris.unibe.ch/73010/8/paper4.pdf

zbMATH Keywords

diffusionLaplace transformimportance samplingMonte Carlo simulationlarge deviationsconditional distributioncompound Poisson risk processcumulant generating functionGerber-Shiu functionsaddlepoint approximations

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Monte Carlo methods (65C05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Diffusion processes (60J60) Large deviations (60F10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (5)

Unnamed Item ⋮ Moment and polynomial bounds for ruin-related quantities in risk theory ⋮ The stability of the probability of ruin ⋮ Unnamed Item ⋮ Uncertainty quantification of stochastic simulation for black-box computer experiments

Cites Work

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• Value at ruin and tail value at ruin of the compound Poisson process with diffusion and efficient computational methods
• On a generalization of the Gerber-Shiu function to path-dependent penalties
• Risk theory for the compound Poisson process that is perturbed by diffusion
• Conjugate processes and the simulation of ruin problems
• Computational methods in risk theory: a matrix-algorithmic approach
• Importance sampling in the Monte Carlo study of sequential tests
• On the discounted penalty at ruin in a jump-diffusion and the perpetual put option
• Four approaches to compute the probability of ruin in the compound Poisson risk process with diffusion
• An operator-based approach to the analysis of ruin-related quantities in jump diffusion risk models
• On a generalization from ruin to default in a Lévy insurance risk model
• Stochastic simulation: Algorithms and analysis
• Erlangian approximation to finite time ruin probabilities in perturbed risk models
• Non-parametric estimation of the Gerber–Shiu function for the Wiener–Poisson risk model
• Modified signed log likelihood ratio
• Saddlepoint expansions for conditional distributions
• Saddle point approximation for the distribution of the sum of independent random variables
• The modified signed likelihood statistic and saddlepoint approximations
• Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix
• A Conditional Saddlepoint Approximation for Testing Problems
• Saddlepoint approximations for the probability of ruin in finite time
• The Gerber–Shiu function in a Sparre Andersen risk process perturbed by diffusion
• Saddlepoint Approximations in Statistics

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