Exponential Family Techniques for the Lognormal Left Tail

DOI10.1111/sjos.12203zbMath1468.62257arXiv1403.4689OpenAlexW2261416239MaRDI QIDQ2821479

Leonardo Rojas-Nandayapa, Jens Ledet Jensen, Soren Asmussen

Publication date: 21 September 2016

Published in: Scandinavian Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.4689

zbMATH Keywords

Laplace transformsaddlepoint approximationimportance samplingLaplace methodlognormal distributionexponential change of measureoutage probabilityLambert \(W\) functionEsscher transformrare event simulationCramér functionVaR (value-at-risk)

Mathematics Subject Classification ID

Applications of statistics to economics (62P20) Characterization and structure theory of statistical distributions (62E10)

Related Items (11)

On the Laplace transform of the lognormal distribution ⋮ On the efficient simulation of the left-tail of the sum of correlated log-normal variates ⋮ Efficient algorithms for tail probabilities of exchangeable lognormal sums ⋮ State-dependent importance sampling for estimating expectations of functionals of sums of independent random variables ⋮ Approximating the Laplace transform of the sum of dependent lognormals ⋮ Approximating the probability density function of a transformation of random variables ⋮ Fast and accurate computation of the distribution of sums of dependent log-normals ⋮ Analysis of Markov chain approximation for Asian options and occupation-time derivatives: Greeks and convergence rates ⋮ On log-normal convolutions: an analytical-numerical method with applications to economic capital determination ⋮ Exponential Family Techniques for the Lognormal Left Tail ⋮ Efficient importance sampling for large sums of independent and identically distributed random variables

Uses Software

• QRM

Cites Work

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• Efficient simulation of tail probabilities of sums of dependent random variables
• On Sums of Conditionally Independent Subexponential Random Variables
• Aggregation of rapidly varying risks and asymptotic independence
• Bounds on the distribution of a sum of independent lognormal random variables
• The log-normal approximation in financial and other computations
• A Normal Limit Theorem for Power Sums of Independent Random Variables

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