The Research Of Option Pricing Problems Based On The Reliability Mathematics Thought

Option pricing problems have always been one of the important problems of finan-cial mathematics research.Black-Scholes formula which developed in the1970s has opened up a new era for the development of financial mat hematics. And then,financial deriva-tives pricing research which based on the standard Brownian motion model has made a great development.However,the special nature of fractional Brownian motion,long-term correlation,dependency,self-similarity has opened up a new research idea for option pric-ing problem.So,the option pricing problem based on fractional Brownian motion model research is becoming a hot spot of current problems.Under the fractional Brownian motion environment,based on the reliability mathe-matics thought,that is,using probability statistics and operational research theories and methods,regards the life-span characteristic of products as the research object,carries on the theory of reliability research.And compared with other methods,the reliability math-ematics thought is not directly from the stock price volatility process,but we regard the Asian option discounted profits and losses as a random variable at the current time,which is convenient for Asian option.Meanwhile,most of Asian option pricing is limited to not pay dividends,In this paper, with the aid of reliability mathematics thought,we prove the new solution for the arithmetic average asian option pricing with dividend.In addition,we also deduce the solution for the European option pricing with dividend.On the conclu-sion,reliability mathematics thought is feasible for the Asian option pricing and European option pricing.