A property of the renewal counting process with application to the finite-time ruin probability

DOI10.1007/s10986-009-9032-1zbMath1185.60098OpenAlexW2003314622MaRDI QIDQ1041393

J. Kočetova, Remigijus Leipus, Jonas Šiaulys

Publication date: 2 December 2009

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-009-9032-1

zbMATH Keywords

large deviationscounting processfinite-time ruin probability

Mathematics Subject Classification ID

Related Items (33)

The finite-time ruin probability for an inhomogeneous renewal risk model ⋮ Web renewal counting processes and their applications in insurance ⋮ Precise large deviation results for sums of sub-exponential claims in a size-dependent renewal risk model ⋮ Second order asymptotics for infinite-time ruin probability in a compound renewal risk model ⋮ Precise large deviations for compound random sums in the presence of dependence structures ⋮ Large deviations for the discounted aggregate claims in time-dependent risk model with constant interest force ⋮ Precise large deviations for dependent random variables with applications to the compound renewal risk model ⋮ Asymptotic sum-ruin probability for a bidimensional risk model with common shock dependence ⋮ Uniform asymptotics for the ruin probabilities in a bidimensional renewal risk model with strongly subexponential claims ⋮ Several properties of a nonstandard renewal counting process and their applications ⋮ Precise large deviations for actual aggregate loss process in a dependent compound customer-arrival-based insurance risk model ⋮ Asymptotics for a time-dependent by-claim model with dependent subexponential claims ⋮ Uniform asymptotics of the finite-time ruin probability for all times ⋮ Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model ⋮ Asymptotic sum-ruin probability for a bidimensional renewal risk model with subexponential claims ⋮ Strong convergence for weighted sums of widely orthant dependent random variables and applications ⋮ Large deviations for sums of claims in a general renewal risk model with the regression dependent structure ⋮ Precise large deviations of aggregate claims in a risk model with regression-type size-dependence ⋮ Lower and upper bounds of large deviation for sums of subexponential claims in a multi-risk model ⋮ Precise large deviations of aggregate claim amount in a dependent renewal risk model ⋮ Precise large deviations of aggregate claims in a size-dependent renewal risk model ⋮ Strong laws for weighted sums of \(m\)-extended negatively dependent random variables and its applications ⋮ Uniform estimates for the finite-time ruin probability in the dependent renewal risk model ⋮ The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables ⋮ A Kesten-type bound for sums of randomly weighted subexponential random variables ⋮ Asymptotics for random-time ruin probability in a time-dependent renewal risk model with subexponential claims ⋮ The uniform local asymptotics for a Lévy process and its overshoot and undershoot ⋮ Precise large deviations for sums of claim-size vectors in a two-dimensional size-dependent renewal risk model ⋮ Moderate deviations for sums of dependent claims in a size-dependent renewal risk model ⋮ Precise large deviations for the aggregate claims in a dependent compound renewal risk model ⋮ A note on the uniform asymptotic behavior of the finite-time ruin probability in a nonstandard renewal risk model ⋮ Asymptotic bounds for precise large deviations in a compound risk model under dependence structures ⋮ The exponential moment tail of inhomogeneous renewal process

Cites Work

• Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails
• Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes
• Precise large deviation results for the total claim amount under subexponential claim sizes
• Large-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilities
• A contribution to large deviations for heavy-tailed random sums
• Asymptotic behaviour of the finite-time ruin probability in renewal risk models
• Large-Deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution
• Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation
• Large deviations of heavy-tailed random sums with applications in insurance and finance
• Note on the Tail Behavior of Random Walk Maxima with Heavy Tails and Negative Drift
• Large deviations for heavy-tailed random sums in compound renewal model

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