(Geometric Brownian Motion)是一种连续时间随机过程,通常用来描述某些财务和经济学领域中的现象,比如股票价格的变化或汇率的波动等。它的特点是在每个时间段内的增长率与当前值成比例,而且这个比例服从正态分布。 几何布朗运动可以用如下的随机微分方程来表示: GBM 其中,St表示在时间 t 时刻的股票价格或其他随机变量...
Geometric Brownian MotionThe usual model for the time-evolution of an asset price $S(t)$ is given by the geometric Brownian motion, represented by the following stochastic differential equation: \begin{eqnarray*} dS(t) = \mu S(t) dt + \sigma S(t) dB(t) \end{eqnarray*} Note that ...
The geometric Brownian motion is the solution of a linear stochastic differential equation in the It sense. If one adds to the drift term a possible nonlinear time-delayed term and starts with a non-negative initial process then the process generated in this way, may hit zero and may ...
18.8.2.2.4 Geometric Brownian motion A geometric Brownian motion B(t) can also be presented as the solution of a stochastic differential equation (SDE), but it has linear drift and diffusion coefficients: dB(t)=μB(t)dt+σB(t)dW(t)ordB(t)B(t)=μdt+σdW(t) If the initial value...
The geometric Brownian motion (GBM) is widely used for modeling stochastic processes, particularly in finance. However, its solutions are constrained by the assumption that the underlying distribution of returns follows a log-normal distribution. This assumption limits the predictive power of GBM, espec...
1)geometric Brownian motion几何布朗运动 1.On condition that price process is geometric Brownian motion,a multi-objective programming model for the portfolio investment is established by minimizing the risk and maximizing the return.在证券的价格过程是几何布朗运动的前提下,建立了最优投资组合的多目标规划模...
Finance GeometricBrownianMotion create new Brownian motion process Calling Sequence Parameters Options Description Examples References Compatibility Calling Sequence GeometricBrownianMotion( , mu , sigma , opts ) GeometricBrownianMotion( , mu , sigma...
Optimal Executive Compensation When Firm Size Follows Geometric Brownian Motion 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 ... Z He - 《Review of Financial Studies》 被引量: 220发表:...
Thus given the constant u and σ, we are able to produce a Geometric Brownian Motion solution through out time interval. 1 Geometric Brownian Motion Model in Financial Market Zhijun Yang 2 Before we start our computer simulation, let explore more mathematical aspects of the geometric brow- nian...
The transition joint probability density function of the solution of geometric Brownian motion equation is presented by a deterministic parabolic time-fractional PDE (FPDE), named time-fractional Fokker-Planck-Kolmogorov equation. The main goal of the present work is to analyze on the numerical ...