Random (Poisson distribution) in the field of financial applications【Abstract】 mathematical finance as a subject. Using a great deal of teaching theory and method study and solve major theories in financial issues, practical problems, and some, such as the pricing of financial innovation. Due to financial problems the complexity of the mathematical knowledge, in addition to the base of knowledge, there are plenty of theories and methods of modern mathematics. In this article we introduce the volume fluctuations in stock price model. Application of Poisson process theory describes the volatility of stock prices, and based on option pricing theory, European call option pricing formula is derived. In the course of financial investment, investors typically shy away from risks, and control the risks in the first place, so we further risk aversion in the market of European call options price range. In order to give investors a more specific reference.【Key words】 stochastic process of compound Poisson process shares traded options pricingAlong with rapid economic development, a variety of financial tools continue to produce. The correct valuation of financial instruments is a necessary condition for effective management of risk, we used the prices of securities described in geometric Brownian motion process is continuous. With fair prices and financial instruments is that they are reasonable and the key. Mathematical finance is 20 centuries later developed a new cross discipline. It is observed with a unique way to meet financial problems, which combine mathematical tools and financial problems. Provide a basis for creative research, solving financial problems and guidance. Through mathematics built die, and theory analysis, and theory is derived, and numerical calculation, quantitative analysis, research and analysis financial trading in the of various problem, to precise to description out financial trading process in the of some behavior and may of results, while research its corresponding of forecast theory, reached avoided financial risk, and achieved financial trading returns maximize of purpose, to makes about financial trading of decision more simple and accurate.Because of financial phenomena studied in mathematical finance strong uncertainty, stochastic process theory as an important branch of probability theory, and are widely used in the financial research. Stochastic process theory include: theory of probability spaces. Poisson process, the updating process, discrete Markov chains and continuous parameters of the Markov chain, theBrown campaign, martingales theory and stochastic integration, stochastic differential equations, and so on. In recent decades, theory and applications of stochastic processes has been developing rapidly. Physics, automation, communication sciences, economics and Management Sciences and many other fields are active figure of the theory of stochastic processes.This stochastic process theory of option pricing using Poisson process theory to the study of regularity of stock price fluctuation in the stock market, consider the impact of transactions on stock prices, stock price process model is constructed. And gives the option of avoiding risks in the investment process.And thePoisson process conceptsDefinitions 1. 1 random process{N t,T≥0} is called the counting process, if theIn time intervals (0,t] occurs in a certain event ( due to a point on the timeline of events, so people called the event ) number. Therefore, a counting process must meet:(1) N t Take non-negative integer values;(2)If s<t, then N s<N t(3) N t In R+=［0，∞）There are continuous and piecewise fetch constants,(4)For s<t, N s,t=N S−N t Is equal to the time (s,t] the number of events occurring in,Said the counting process{N t,T≥0} has independent increments. If it's in any finite number of disjoint events that occur in the time interval of a few independent of each other, said the counting process{N t,T≥0} with stationary increments, if at any time the probability distribution of the number of events that occurred in the interval depends only on the length of the interval, and has nothing to do with its location. That for any0≤t1≤t2And s≥0 Incremental N t1,t2 And N t1+s,t2+s Have the same probability distribution.Definitions 1. 2 counting process{N t,T≥0} is called intensity ( or speed )The homogeneous Poisson process if it meets the following conditions:(1) P(N0=0) =1，(2)Has independent increments.(3)For any 0s<t , N s,t=N S−N t With parameter(t--s) The Poisson distribution, whichDefinitions 1. 3 count process{,T≥0} is called the Poisson process, the argument is，λ>0 If(1) N0=0；(2)Processes with stationary independent increments.IfYou can proveThat is, N s+t−N t Has mean m (t+s) m (t) of the Poisson distribution.Non-homogeneous Poisson process is important because no longer requires a stationary increments, allowing the possibility of events at certain times than others.Dang strength(t) Territories can be non-homogeneous Poisson process is regardedas a homogeneous Poisson random sampling. Established specifically to meet(t) ≤And, for all t≥0 and considered a strength for Poisson process. Set up the process at time t with probability(t) /Count, was count of events is the process of withintensity function(t) Non-homogeneous Poisson process.Second, based on complex Poisson process model of stock prices1. model constructionAssumptions in the stock market, a yin and the strength of each transaction is asequence of independent identically distributed random variables. We use I trade intensity, then for any i>O,Have the same distribution. Set the stock tradesIs a parameter for(λ>o) Poisson process, its trading volume for the compound Poisson process.We believe that the trading volume in the stock market will have an impact on stock prices, established the following model to simulate the volatility. Setting the time parameter is set to T=[o,∞)。