Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
Large deviations of heavy-tailed random sums with applications in insurance and finance - MaRDI portal

Large deviations of heavy-tailed random sums with applications in insurance and finance

From MaRDI portal
Publication:4358581

DOI10.2307/3215371zbMath0903.60021OpenAlexW2142226753MaRDI QIDQ4358581

Thomas Mikosch, Claudia Klüppelberg

Publication date: 5 January 1999

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3215371




Related Items (94)

Precise large deviations for sums of random vectors with dependent components of consistently varying tailsLarge deviation estimates involving deformed exponential functionsWeb renewal counting processes and their applications in insurancePrecise large deviation results for sums of sub-exponential claims in a size-dependent renewal risk modelPrecise Large Deviations for Sums of Negatively Dependent Random Variables with Common Long-Tailed DistributionsPrecise large deviation for sums of sub-exponential claims with the \(m\)-dependent semi-Markov type structurePrecise large deviations of aggregate claims in a discrete-time risk model with Poisson ARCH claim-number processAsymptotic results for the sum of dependent non-identically distributed random variablesPrecise Large Deviations for the Actual Aggregate Loss ProcessModerate deviations for random sums of heavy-tailed random variablesPrecise large deviations for sums of random variables with consistently varying tailsElementary renewal theorems for widely dependent random variables with applications to precise large deviationsPrecise large deviations for strong subexponential distributions and applications on a multi risk modelPrecise deviations for Cox processes with a shot noise intensityPrecise large deviations for compound random sums in the presence of dependence structuresPrecise large deviations of aggregate claims with arbitrary dependence between claim sizes and waiting timesPrecise large deviations for negatively associated random variables with consistently varying tailsLarge deviations results for subexponential tails, with applications to insurance riskPrecise large deviations for dependent random variables with applications to the compound renewal risk modelSeveral properties of a nonstandard renewal counting process and their applicationsAsymptotic behaviour of the finite-time ruin probability under subexponential claim sizesPrecise large deviations for sums of negatively associated random variables with common dominatedly varying tailsA large deviation result for aggregate claims with dependent claim occurrencesLarge deviations for random sums of differences between two sequences of random variables with applications to risk theoryPrecise local large deviations for heavy-tailed random sums with applications to risk modelsLarge deviations for random sums of negatively dependent random variables with consistently varying tailsPrecise large deviations for consistently varying-tailed distributions in the compound renewal risk modelPrecise large deviations for long-tailed distributionsPrecise large deviations for actual aggregate loss process in a dependent compound customer-arrival-based insurance risk modelPrecise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk modelStrong convergence for weighted sums of widely orthant dependent random variables and applicationsLarge deviations of aggregate amount of claims in compound risk model with arbitrary dependence between claim sizes and waiting timesPrecise large deviations for a customer-based individual risk modelPrecise large deviations for aggregate claims of a compound renewal risk model with arbitrary dependence between claim sizes and waiting timesPrecise large deviations of random sums in presence of negative dependence and consistent variationPrecise large deviations for random sums of END real-valued random variables with consistent variationPrecise large deviations for aggregate claims in a multidimensional risk model with arbitrarily dependent claims and accident-arriving timesPrecise large deviations of aggregate claims in a risk model with regression-type size-dependenceLower bounds of large deviation for sums of long-tailed claims in a multi-risk modelLower and upper bounds of large deviation for sums of subexponential claims in a multi-risk modelPrecise large deviations of aggregate claim amount in a dependent renewal risk modelPrecise large deviations of aggregate claims in a compound size-dependent renewal risk modelPrecise large deviations for the difference of two sums of WUOD and non identically distributed random variables with dominatedly varying tailsPrecise large deviations for the difference of two sums of END random variables with heavy tailsPrecise large deviations of aggregate claims in a size-dependent renewal risk modelUnnamed ItemPrecise large deviations for random sums of END random variables with dominated variationPrecise large deviations of aggregate claims with dominated variation in dependent multi-risk modelsLongevity bond premiums: the extreme value approach and risk cubic pricingStrong laws for weighted sums of \(m\)-extended negatively dependent random variables and its applicationsPrecise large deviation results for the total claim amount under subexponential claim sizesGumbel and Fréchet convergence of the maxima of independent random walksMarkovian risk processPrecise large deviations of aggregate claims in a risk model with size dependence and non stationary arrivalsLindeberg's method for moderate deviations and random summationLarge-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilitiesPrecise large deviations for sums of WUOD and φ-mixing random variables with dominated variationLarge deviations for sums of random vectors attracted to operator semi-stable lawsPrecise large deviations for randomly weighted sums of negatively dependent random variables with consistently varying tailsMarkov Chain Monte Carlo for Computing Rare-Event Probabilities for a Heavy-Tailed Random WalkLarge deviations for heavy-tailed random sums in compound renewal modelThe general principle for precise large deviations of heavy-tailed random sumsLarge deviations for randomly weighted sums with dominantly varying tails and widely orthant dependent structurePrecise large deviations for generalized dependent compound renewal risk model with consistent variationFinite- and infinite-time ruin probabilities in the presence of stochastic returns on investmentsPricing catastrophe insurance products based on actually reported claimsRuin probabilities for risk processes with non-stationary arrivals and subexponential claimsLarge deviations for generalized compound Poisson risk models and its bankruptcy momentsApproximating the moments of marginals of high-dimensional distributionsNecessary and sufficient conditions for moderate deviations of dependent random variables with heavy tailsA sharp inequality for the tail probabilities of sums of i.i.d. r.v.'s with dominatedly varying tailsHeavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal ModelPrecise large deviations for the prospective-loss processPrecise large deviation for the difference of two sums of random variablesAsymptotic behaviour of the finite-time ruin probability in renewal risk modelsPrecise large deviations for sums of claim-size vectors in a two-dimensional size-dependent renewal risk modelLarge deviations for sum of UEND andφ-mixing random variables with heavy tailsPrecise Large Deviations for Sums of Independent Random Variables with Consistently Varying TailsPrecise large deviations for aggregate claimsComment on the work of Zhang et al. ``Precise large deviations of aggregate claims in a size-dependent renewal risk model with stopping time claim-number processPrecise large deviations for sums of two-dimensional random vectors with dependent components of heavy tailsA property of the renewal counting process with application to the finite-time ruin probabilitySecond order corrections for the limits of normalized ruin times in the presence of heavy tailsRuin probability of the renewal model with risky investment and large claimsFinite Time Ruin Probability of the Compound Renewal Model with Constant Interest Rate and Weakly Negatively Dependent Claims with Heavy TailsAsymptotic bounds for precise large deviations in a compound risk model under dependence structuresAsymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claimsFinite time ruin probabilities and large deviations for generalized compound binomial risk modelsThe exponential moment tail of inhomogeneous renewal processCritical fluctuations in renewal models of statistical mechanicsPrecise Large Deviations for Sums of Random Variables with Consistent Variation in Dependent Multi-Risk ModelsA contribution to large deviations for heavy-tailed random sumsPrecise large deviations of aggregate loss process in a risk model based on the policy entrance processStatistical fluctuations under resetting: rigorous results




This page was built for publication: Large deviations of heavy-tailed random sums with applications in insurance and finance