A saddlepoint approximation to the distribution of inhomogeneous discounted compound Poisson processes

DOI10.1007/s11009-008-9116-0zbMath1202.60072OpenAlexW2078863505MaRDI QIDQ708790

Riccardo Gatto

Publication date: 14 October 2010

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

Full work available at URL: https://boris.unibe.ch/118120/

zbMATH Keywords

Monte Carlointerest rateintensity functioncumulant generating functionshot-noise processtotal claim amount

Mathematics Subject Classification ID

Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (7)

Gamma-related Ornstein–Uhlenbeck processes and their simulation* ⋮ Saddlepoint approximations to tail probabilities and quantiles of inhomogeneous discounted compound Poisson processes with periodic intensity functions ⋮ Four approaches to compute the probability of ruin in the compound Poisson risk process with diffusion ⋮ Conditional, non-homogeneous and doubly stochastic compound Poisson processes with stochastic discounted claims ⋮ Values and tail values at risk of doubly compound inhomogeneous and contagious aggregate loss processes ⋮ Value at ruin and tail value at ruin of the compound Poisson process with diffusion and efficient computational methods ⋮ A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes

Cites Work

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• Non-life insurance mathematics. An introduction with stochastic processes.
• Simple approximations of ruin probabilities
• Approximations for compound Poisson and Pólya processes
• Saddle point approximation for the distribution of the sum of independent random variables
• Saddlepoint approximations to the distribution of the total claim amount in some recent risk models
• Ruin theory with stochastic return on investments
• Tail Probability Approximations
• The total claims distribution under inflationary conditions
• Saddlepoint Approximations in Statistics

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