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.

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,...

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...

Let {X,Xn,n≥1} be a sequence of i.i.d. random variables, and set Sn=X1+⋯+Xn. For 1<p≤3/2, if EX=0, EX2=1 and E[|X|2p(log+|X|)−p]<∞, we prove that limε↘0ε1/2∑n≥2np−2P(|Sn|≥(2p−2+ε)nlogn)=2p−1, thus extending a result by Spătaru (2004). For 1<p≤3/2 and δ>0, we establish conditions for the convergence of the related series ∑n≥2np−2P(|Sn|≥(2p−2)nlogn+δn1/2loglogn(2p−2)nlogn), and derive its precise asymptotic as δ↘1/2.