We study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two state quantum systems (or polarised light) undergoing random evolution. Our results are also relevant to recent experiments which observe the Brownian motion of molecules on c...

In this paper, we are concerned with the largeN limit of linear combinations of entries of Brownian motions on the group of N ×N unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one. Various scales of time are concerned, giving rise to various limit processes, in relation to the geometric construction of the unitary Brownian motion. As an applicat...

We numerically price the financial contracts named turbo warrant that were released early in 2005. They have been studied mathematically in [3] where explicit pricing formulas for the Geometric Brownian motion were derived. For more general underlying stochastic processes we have no analytical formulas and numerical methods are necessary. In this work two different methods are compared, stochas...

In this paper the option value of waiting under scientific uncertainty will be derived using the difference between the geometric Brownian motion and the mean reverting process by applying contingent claim analysis. The results will be compared with those generated by either using a geometric Brownian motion or a mean-reverting process only. An example based on the decision problem whether or n...

in this paper, natural convection heat transfer over a vertical plate in a darcy porous medium saturated with a nanofluid subject to heat generation/absorption was theoretically studied. the governing partial differential equations were transformed to a set of ordinary differential equations using similarity transformations and solved using finite difference method. the influence of parametric ...

We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional generalization of a theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion. It is based on a mapping which can be regarded as a geometric variant of the RSK correspondence....

We solve explicitly the Almgren–Chriss optimal liquidation problem where stock price process follows a geometric Brownian motion. Our technique is to work in terms of cash and use functional analysis tools. show that this framework extends readily case stochastic drift for portfolio.

Cash flows are often modeled using the random geometric growth model (geometric Brownian motion). One of the reasons for using this model is that it is simple to implement and it is a reasonable approximation to random growth cash flows such as stock prices. For this model the volatility of the cash flow grows multiplicatively over time. This multiplicative characteristic is shared by the usual...