In this article we consider the efficient estimation of the tail distribution of the maximum of correlated normal random variables. We show that the currently recommended Monte Carlo estimator has difficulties in quantifying its precision, because its sample variance estimator is an inefficient...

Fitting parametric models or the use of the empirical cumulative distribution function are problematic when it comes to the estimation of tail probabilities from small samples. A possible remedy is to fuse or combine the small samples with additional data from external sources and base the...

Fitting parametric models or the use of the empirical cumulative distribution function are problematic when it comes to the estimation of tail probabilities from small samples. A possible remedy is to fuse or combine the small samples with additional data from external sources and base the...

The papers (Forde and Jacquier in Finance Stoch. 15:755–780, <CitationRef CitationID="CR1">2011</CitationRef>; Forde et al. in Finance Stoch. 15:781–784, <CitationRef CitationID="CR2">2011</CitationRef>) study large-time behaviour of the price process in the Heston model. This note corrects typos in Forde and Jacquier (Finance Stoch. 15:755–780, <CitationRef CitationID="CR1">2011</CitationRef>), Forde et al. (Finance...</citationref></citationref></citationref>

Assuming that the claim sizes of an insurance company have a common distribution with gamma-like tail, we study the asymptotic tail behaviour of the reinsured amounts under the ECOMOR and LCR reinsurance treaties, respectively. Our novel results include a precise asymptotic expansion for the...

The tails of the distribution of a mean zero, variance σ2 random variable Y satisfy concentration of measure inequalities of the form P(Y≥t)≤exp(−B(t)) forB(t)=t22(σ2+ct)for  t≥0,andB(t)=tc(logt−loglogt−σ2c)for  te whenever there exists a zero biased coupling of Y bounded by c,...

A well-known longstanding conjecture on the supremum of the tails of normalized sums of independent Rademacher random variables is disproved. A special case of this conjecture was recently disproved by A. Zhubr.