In this paper, we are concerned with Reflected Geometric Brownian Motion (RGBM) with two barriers. And the stationary distribution of RGBM is derived by Markovian infinitesimal Generator method. Consequently the first passage time of RGBM is also discussed.

The author shows how to compute correlation coefficients in an ndimensional geometric Brownian motion model for foreign exchange rates, interprets the result geometrically and applies it to eliminate correlation risk when trading multi-asset options

A theory of integration for anticommuting paths is described. This is combined with standard Itô calculus to give a geometric theory of Brownian paths on curved supermanifolds. This lecture concerns a generalisation of Brownian motion and Itô calculus to include paths in spaces of anticommuting variables. The motivation for this work comes originally from physics, where anticommuting variables ...

We study the effects of stochastic resetting on geometric Brownian motion (GBM), a canonical multiplicative process for non-stationary and non-ergodic dynamics. Resetting is sudden interruption process, which consecutively renews its show that, although renders GBM stationary, resulting remains non-ergodic. Quite surprisingly, effect pivotal in manifesting behavior. In particular, we observe th...

An important determinant of option prices is the elasticity of the pricing kernel used to price all claims in the economy. In this paper, we rst show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the ...

Abstract We prove a number of results relating exit times planar Brownian motion with the geometric properties domains in question. Included are proofs conformal invariance moduli rectangles and annuli using motion; similarly probabilistic some recent Karafyllia on harmonic measure starlike domains; examples their complements which simultaneously large when measured by moments time motion, smal...