1)  geometric Brownian motion

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.

2.
Assuming the underlying stock asset follows geometric Brownian motion,the models of minimal pricing of European stock options were made.

3.
On the assumption that investment fund follows geometric Brownian motion,the pricing model of a short-period insurance contract that is affected by its investment profit is established.

2)  Geometric Brown Motion

1.
Using the Geometric Brown Motion model we simulate the fluctuation of stock price during a period of time and draw its curve,then compare the curve with that of the real stock price,we find that the fluctuation of stock price is almost consistent with the Geometric Brown Motion intuitively.

3)  geometrical Brownian motion

1.
The impulse consumption control strategy of the problem is governed by a mixed process-geometrical Brownian motion and a Poisson process.

4)  Geometry Brownian Movement

1.
It based on below basic supposition, (1) the primary property prices obey the geometry Brownian movement(2) non- risk interest rate r is constant, (3) the primary property does not pay the dividend, (4) not to pay the transaction cost and the tax revenue, (5) no the chance of arbitrage.

2.
When built the B-S formula in the complete market, the stock prices are assumed to obey geometry Brownian movement, however, it is inconsistent with the results of the substantial evidence to be tested, so the options pricing in the incomplete market can’t be assumed to obey geometry Brownian movement.

5)  'Brown Movement' with jumping

6)  geometric fractional Brownian motion

1.
Based on their work,this paper obtains European option pricing formula when underlying assets are driven by geometric fractional Brownian motion,and we point out geometric Brownian motion is a special case of our model.

2.
Pricing reload option in geometric fractional Brownian motion environment is investigated in the paper.

 布朗运动Brownian movement   悬浮在液体或气体中的微小粒子所作的不停顿的无规则运动。例如，在显微镜下观察悬浮在水中的藤黄粉、花粉微粒，或在无风情形观察空气中的烟粒、尘埃时都会看到这种运动。温度越高，运动越激烈。它是1827年植物学家R.布朗首先发现的。作布朗运动的粒子非常微小，直径约10-7～10-5米， 在周围液体或气体分子的碰撞下，产生一种涨落不定的净作用力，导致微粒的布朗运动。如果布朗粒子相互碰撞的机会很少，可以看成是巨大分子组成的理想气体，则在重力场中达到热平衡后，其数密度按高度的分布应遵循玻耳兹曼分布。J.B.佩兰的实验证实了这一点，并由此相当精确地测定了阿伏伽德罗常量及一系列与微粒有关的数据。1905年A.爱因斯坦根据扩散方程建立了布朗运动的统计理论。布朗运动的发现、实验研究和理论分析间接地证实了分子的无规则热运动，对于气体动理论的建立以及确认物质结构的原子性具有重要意义，并且推动统计物理学特别是涨落理论的发展。由于布朗运动代表一种随机涨落现象，它的理论对于仪表测量精度限制的研究以及高倍放大电讯电路中背景噪声的研究等有广泛应用。