Saddlepoint approximations to tail probabilities and quantiles of inhomogeneous discounted compound Poisson processes with periodic intensity functions

DOI10.1007/s11009-011-9219-xzbMath1258.91102OpenAlexW2068872785MaRDI QIDQ1930449

Riccardo Gatto

Publication date: 11 January 2013

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

Full work available at URL: https://boris.unibe.ch/17994/

zbMATH Keywords

Monte Carlo simulationFourier seriesvon Mises distributioninterest ratecumulant generating functiontrigonometric polynomialcircular distributiontotal claim amountflat-topped distributionwrapped \(\alpha \)-stable distribution

Mathematics Subject Classification ID

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

Related Items (3)

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 ⋮ Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

Uses Software

• CircStats
• circular

Cites Work

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• The generalized von Mises distribution
• Ruin probabilities and aggregrate claims distributions for shot noise Cox processes
• Saddle point approximation for the distribution of the sum of independent random variables
• The modified signed likelihood statistic and saddlepoint approximations
• Saddlepoint Approximations in Statistics
• Moment generating functions of compound renewal sums with discounted claims

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