The convergence of properly time-scaled and normalized maxima of independent standard Brownian motions to the Brown–Resnick process is well-known in the literature. In this paper, we study the extremal functional behavior of non-Gaussian processes, namely squared Bessel processes and scalar...

Introducing certain singularities, we generalize the class of one-dimensional stochastic differential equations with so-called generalized drift. Equations with generalized drift, well-known in the literature, possess a drift that is described by the semimartingale local time of the unknown...

This paper provides a novel proof for the sufficiency of certain well-known criteria that guarantee the martingale property of a continuous, nonnegative local martingale. More precisely, it is shown that generalizations of Novikov’s condition and Kazamaki’s criterion follow directly from the...

The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values...

In this note, we present some refinements of the well-known domination inequalities. Let X be an adapted positive cadlag process dominated by a predictable increasing process A with A0=0. We derive some sharper constants in the inequalities. For the widely used inequality...

We consider the constant elasticity of variance (CEV) process, reviewing the relationships between its transition density and that of the non-central chi-squared distribution. When the CEV parameter exceeds one, the forward price process is a strictly local martingale, and the price of a plain...