We consider samples of geometric random variables and find the average size of the descent after the first and last maximal values. These are asymptotically but not exactly equal, with the descent after the last maximum being slightly larger than that after the first. Thereafter we calculate the...

We consider a new problem of constructing some required structures in digraphs, where all arcs installed in such required structures are supposed to be cut from some pieces of a specific material of length L. Formally, we consider the model: a digraph D=(V, A; w), a structure S and a specific...

We derive exact and asymptotic formulas for the probability that a symmetric n×n matrix with unit diagonal and upper diagonal elements i.i.d. uniform on (−1,1) is positive definite (and thus a “random correlation matrix”): this is almost never the case for n≥6.

In this paper we propose a simple non-parametric calibration procedure of option prices based on the short term asymptotics of implied volatilities. The approximation formula is derived for a general one factor jump-diffusion specification nesting most of the theoretical models typically used...

The pricing of collateralized debt obligations (CDOs) and other basket credit derivatives is contingent upon (i) a realistic modelling of the firms' default times and the correlation between them, and (ii) efficient computational methods for computing the portfolio loss distribution from the...

In statistical analyses the complexity of a chosen model is often related to the size of available data. One important question is whether the asymptotic distribution of the parameter estimates normally derived by taking the sample size to infinity for a fixed number of parameters would remain...

We derive a closed-form asymptotic expansion formula for option implied volatility under a two-factor jump-diffusion stochastic volatility model when time-to-maturity is small. Based on numerical experiments we describe the range of time-to-maturity and moneyness for which the approximation is...