This paper summarizes the study on options pricing in view of quantum finance,such as the path integrals approach, the gauge theory of arbitrage, and the quantum model of binomial option pricing.

Then, based on the analysis of characters of strategic investment in mobile telecommunication field, an analysis model of appraisal strategy investment decision-making has been constructed by applying the binomial options tree method to evaluate.

The paper expounds the application of real option in the financing decision of startup firms in uncertainty on the theoretical basis of riskneutral pricing approach and binomial model.

Based on the process of the development of European option pricing,its mathematical models and pricing formulae are introduced in this paper.

The main aims of the dissertion are:(1)To establish the fractional mode of option pricing with respect to a fractional Brownian motion Bn(t) with Hurst exponent H ∈ [5,1);(2)To establish the generalized mode of option pricing and to give the analytical solution for European option pricing;(3)To establish the mode of option pricing with respect to a stochastic process X(t) - ta g(i, T)dB(r)ai.

In this paper,based on the assumption of underlying asset \'s Brownian motion and poisson motion,in the real financial market with transaction costs,the model of European option pricing is obtained by using Ito formula and hedging strategy.