‎In this paper Lie symmetry analysis is applied to find new‎ solution for Fokker Plank equation of geometric Brownian motion‎. This analysis classifies the solution format of the Fokker Plank‎ ‎equation‎.

In sharp contrast to the dominant real option valuation that assumes a stochastic process for an investment’s capital value, this paper demonstrates the valuation of a real option assuming that cash flow follows a stochastic process. We show that this method is at least equally effective and sometimes more intuitive. We note that, in a discounted cash flow (DCF) framework, only when certain con...

Mixed fractional Brownian motion (MFBM) is a linear combination of and an independent which may overcome the problem arbitrage, while jump process in time series another to be address modeling stock prices. This study models call warrants with MFBM includes its dynamics. The pricing formula for warrant mixed-fractional jump, obtained via quasi-conditional expectation risk-neutral valuation.

In this paper, we consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. We show that we can describe the evolution of the distance between the two processes with a stochastic differential equation. This S.D.E. possesses a jump component driven by the excursion process of one of the two skew Brownian motions. U...

We present a formula for the corner points of the multi-dimensional Hausdorff polytopes and show how this result can be used to improve linear programming models for computing, e. g., moments of exit time distributions of diffusion processes. Specifically, we compute the mean exit time of two-dimensional Brownian motion from the unit square, as well as higher moments of the exit time of time-sp...

The joint distribution of a geometric Brownian motion and its time-integral was derived in seminal paper by Yor (1992) using Lamperti’s transformation, leading to explicit solutions terms modified Bessel functions. In this paper, we revisit classic result the simple Laplace transform approach connection Heun differential equation. We extend methodology with affine drift show that process can be...

‎In this paper we study the dynamics of the 2D-motion of a particle of monolayer‎. First we consider the usual physical time component and the plan manifold R2, having the polar coordinates. Then a geometric approach to nonholonomic constrained mechanical systems is applied to a problem from the two dimensional geometric dynamics of the Langmuir-Blodgett monolayer‎. We consider a constraint sub...

We establish a uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains. Exact Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are given. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also mentioned. AMS Mathematics Subject Classification (2000): Primary 60G17, 60J60; ...