We study drawdowns and rallies of Brownian motion. A rally is defined as the difference of the present value of the Brownian motion and its historical minimum, while the drawdown is defined as the difference of the historical maximum and its present value. This paper determines the probability that a drawdown of a units precedes a rally of b units. We apply this result to examine stock market c...

Right-tailed distributions are very important in many applications. There studies estimating the tail index. In this paper, we will estimate parameter  using three (the Direct, Bootstrap and Double Bootstrap) methods. Our aim is to illustrate best way   -stable with simulation real data for daily Iraqi financial market dataset.

In this paper scientific uncertainty is defined as the impossibility to choose the correct stochastic process for the value of a public policy. The real option value of waiting under scientific uncertainty is derived using the difference between the geometric Brownian motion and the mean reverting process by applying contingent claim analysis. The results are compared with those generated by ei...

The CFD simulation has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosure, whose dimension, width height length (mm), is 40 40 90, respectively. The nanofluid used in the present study is -water with various volumetric fractions of the alumina nanoparticles ranging from 0-3%. The Rayleigh number is . Fluent v6.3 is used to simulate nanofluid ...

We obtain the Laplace transform and integrability properties of the integral over R+ of the call quantity associated with geometric Brownian motion with negative drift, thus adding a new element to the list of already studied Brownian perpetuities.

This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.

‎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.

We generalize the notion of brownian bridge. More precisely, we study a standard brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak solutions of stochastic differential equations which we call conditioned stochastic differential equations. The link with the theory of initial enlargement of filtration is made and after a general pre...