The total claims distribution under inflationary conditions

DOI10.1080/03461238.1989.10413851zbMath0679.62094OpenAlexW2000851948MaRDI QIDQ4729222

Gordon E. Willmot

Publication date: 1989

Published in: Scandinavian Actuarial Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03461238.1989.10413851

zbMATH Keywords

inflationcompound distributionorder statistic propertyshot noise processtotal claims distributionexponential claim sizesmixed Poisson claim number processesregular variation of the tailtime dependent claim amounts

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Exact distribution theory in statistics (62E15) Statistical distribution theory (62E99)

Related Items (31)

Refinements and distributional generalizations of Lundberg's inequality ⋮ Arbitrage-free premium calculation for extreme losses using the shot noise process and the Esscher transform ⋮ The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding ⋮ On the analysis of a class of loss models incorporating time dependence ⋮ Moments of discounted aggregate claims with dependence based on Spearman copula ⋮ Moments of claims in a Markovian environment ⋮ Bivariate compound renewal sums with discounted claims ⋮ Insurance risk capital for the Sparre Andersen model with geometric Lévy stochastic returns ⋮ The distribution of discounted compound PH-renewal processes ⋮ Conditional, non-homogeneous and doubly stochastic compound Poisson processes with stochastic discounted claims ⋮ A note on discounted compound renewal sums under dependency ⋮ Pricing compound Poisson processes with the Farlie-Gumbel-Morgenstern dependence structure ⋮ A multivariate aggregate loss model ⋮ Catastrophe risk management with counterparty risk using alternative instruments ⋮ Some specific density functions of aggregated discounted claims with dependent risks ⋮ Recursive Moments of Compound Renewal Sums with Discounted Claims ⋮ Moments of compound renewal sums with discounted claims ⋮ Comparison of individual risk models ⋮ A saddlepoint approximation to the distribution of inhomogeneous discounted compound Poisson processes ⋮ Ruin and deficit under claim arrivals with the order statistics property ⋮ Two-sided exit problems in the ordered risk model ⋮ Jump diffusion processes and their applications in insurance and finance ⋮ On multivariate discounted compound renewal sums with time-dependent claims in the presence of reporting/payment delays ⋮ Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators ⋮ The order-statistic claim process with dependent claim frequencies and severities ⋮ Mixtures of tails in clustered automobile collision claims ⋮ The construction of a quadratic predictor of the discounted renewal claims with dependence ⋮ Covariance of discounted compound renewal sums with a stochastic interest rate ⋮ Joint moments of discounted compound renewal sums ⋮ Ruin probabilities in the presence of heavy-tails and interest rates ⋮ On the Laplace Transform of the Aggregate Discounted Claims with Markovian Arrivals

Cites Work

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• Approximations for stop-loss premiums
• Classical risk theory in an economic environment
• High-order methods for the numerical solution of Volterra integro- differential equations
• Probability of ruin for a risk process with claims cost inflation
• A characterization of order statistic point processes that are mixed Poisson processes and mixed sample processes simultaneously
• An order statistic characterization of the poisson renewal process
• On the characterization of point processes with the order statistic property without the moment condition
• Subexponentiality and infinite divisibility
• On the characterization of point processes with the order statistic property

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