Tail behavior of supremum of a random walk when Cramér's condition fails
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Publication:2259115
DOI10.1007/s11464-013-0302-1zbMath1322.60053OpenAlexW2059174765MaRDI QIDQ2259115
Publication date: 27 February 2015
Published in: Frontiers of Mathematics in China (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11464-013-0302-1
asymptotic estimaterandom walkruin probabilityrenewal risk modelsupremumexponential distribution classO-subexponential distribution class
Sums of independent random variables; random walks (60G50) Probability distributions: general theory (60E05) Limit theorems in probability theory (60F99) Renewal theory (60K05)
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Cites Work
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- Uniform asymptotics of the finite-time ruin probability for all times
- New examples of heavy-tailed O-subexponential distributions and related closure properties
- Some properties of the exponential distribution class with applications to risk theory
- Random walks with non-convolution equivalent increments and their applications
- Finite-time ruin probability of a nonstandard compound renewal risk model with constant force of interest
- The full solution of the convolution closure problem for convolution- equivalent distributions
- Asymptotics for ruin probability of some negatively dependent risk models with a constant interest rate and dominatedly-varying-tailed claims
- Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes
- Convolution equivalence and distributions of random sums
- Ratio of the tail of an infinitely divisible distribution on the line to that of its Lévy measure
- Lower limits and upper limits for tails of random sums supported on \(\mathbb R\)
- Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications
- On lower limits and equivalences for distribution tails of randomly stopped sums
- Equivalent conditions of asymptotics for the density of the supremum of a random walk in the Intermediate case
- Estimates for the probability of ruin with special emphasis on the possibility of large claims
- On convolution tails
- Asymptotic behaviour of Wiener-Hopf factors of a random walk
- Degeneracy properties of subcritical branching processes
- Subexponential distributions and characterizations of related classes
- Asymptotic ordering of distribution functions and convolution semigroups
- Functions of probability measures
- Asymptotics for sums of random variables with local subexponential behaviour
- A local limit theorem for random walk maxima with heavy tails
- Some discussions on the class \({\mathcal L} (\gamma)\)
- Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models
- Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate
- On distribution tail of the maximum of a random walk
- Infinite divisibility and generalized subexponentiality
- Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation
- The Uniform Local Asymptotics of the Overshoot of a Random Walk with Heavy-Tailed Increments
- On the non-closure under convolution of the subexponential family
- Ruin probabilities in the presence of heavy-tails and interest rates
- Convolution equivalence and infinite divisibility
- Some asymptotic results for transient random walks
- An Introduction to Heavy-Tailed and Subexponential Distributions
- Asymptotics for the moments of the overshoot and undershoot of a random walk
- Asymptotics of the density of the supremum of a random walk with heavy-tailed increments
