The application of the model geometric Brownian motion (GBM) for problem modeling and forecasting prices cryptocurrencies is analyzed. For prediction solution stochastic differential equation GBM used, which has a linear drift diffusion coefficients. Different scenarios price movement are considered.
 Keywords: (GBM), modeling, forecasting, cryptocurrency.

A new explicit form is provided for the solution of optimal stopping problems involving a multidimensional geometric Brownian motion. free-boundary value approach adopted and function obtained via fundamental methods. There are many applications valuation perpetual options American style, which interest finance managerial decisions.

In the case of early exercise of an American-style call option, we consider the issue of the existence of a “treshhold value,” namely a boundary which, once exceeded, early exercise is optimal for all values of the underlying asset which exceed that value. We discuss optimal exercise thresholds for call options for two-period models, under alternate contexts: geometric Brownian motion vs. mean-...

This paper presents a study of the Hurst index estimation in the case of fractional Ornstein–Uhlenbeck and geometric Brownian motion models. The performance of the estimators is studied both with respect to the value of the Hurst index and the length of sample paths.

This paper studies a continuous-time agency model in which the agent controls the drift of the geometric Brownian motion firm size. The changing firm size generates partial incentives, analogous to awarding the agent equity shares according to her continuation payoff. When the agent is as patient as investors, performance-based stock grants implement the optimal contract. Our model generates a ...

The geometric Brownian motion (GBM) process is frequently invoked as a model for such diverse quantities as stock prices, natural resource prices, and the growth in demand for products or services. We discuss a process for checking whether a given time series follows the GBM process. Methods to remove seasonal variation from such a time series are also analyzed. Of four industries studied, the ...

For a simple model of a stock, whose stock price is a geometric Brownian motion in which the drift rate changes back and forth between positive and negative values, optimal selling times are computed. An infinite optimal selling time meaning you should just hold the stock.

Abstract. In this research we try to consider the problem of applying the Nonhomogeneous Poisson process to trends of economic development. More specifically, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean and the variance of the modified process ...

We show that the mixed phase space dynamics of a typical smooth Hamiltonian system universally leads to a sustained exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of geometric Brownian motion with a positive drift, and relate it to the steady entropy increase after each period of the parameters variation.

We develop a probabilistic theory for conversion of A→ B processes for a model Temporal Analysis of Products (TAP)-like experiments based on the general theory of Brownian motion with killing and the Feynman-Kac formula. Initial experimental testing for systems with a single catalyst particle is given, as well as numerical experiments for two-particle catalyst systems in simple geometric config...