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.

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

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.

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

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.

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.

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.