The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of Brownian motion, the optimality fails in ge...

Abstract. This paper studies the law of any power of the integral of geometric Brownian motion over any finite time interval. As its main results, two integral representations for this law are derived. This is by enhancing the Laplace transform ansatz of [Y] with complex analytic methods, which is the main methodological contribution of the paper. The one of our integrals has a similar structur...

Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by nonergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average. A common tactic for bringing time averages closer to ensemble averages is diversifi...

This paper generalizes earlier work by G. Larcher and the author about hedging with short-term futures contracts, a problem which was considered in connection with the debacle of the German company Metallgesellschaft. While the original problem corresponded to the simplest possible model for the price process, i.e. Brownian motion, we give here solutions to more general models, i.e. a mean reve...

We give a geometric derivation of SLE(κ, ρ) in terms of con-formally invariant random growing compact subsets of polygons. The parameters ρ j are related to the exterior angles of the polygons. We also show that SLE(κ, ρ) can be generated by a metric Brownian motion , where metric and Brownian motion are coupled and the metric is a pull-back metric of the Euclidean metric of an evolving polygon.

Effect of nonlinear thermal radiation on the unsteady magnetohydrodynamic slip flow of Casson fluid between parallel disks in the presence of thermophoresis and Brownian motion effects are investigated numerically. A similarity transformation is employed to reduce the governing partial differential equations into ordinary differential equations. Further, Runge-Kutta and Newton’s methods are ado...

exchange rate prediction, as one of the main variables in macroeconomics, has been one of the aims of the economic research for a long time. for modeling and predicting exchange rate we apply stochastic differential equation, specifically we use geometric brownian motion (gbm) and jump-diffusion process (mjdp) attributed to merton. we show that the result of simulation based on gbm and mjdp out...

This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number an...