The Optimal Investment Proportion Of Binary Options Base On The Kelly Criterion

This paper studies binary options Optimum Investment Proportion based on Kelly criterion.The first chapter is an introduction, a brief introduction about the Kelly formula research background and some important research results and applications from Kelly formula proposed since, and gives the main results of this study.The second chapter is preliminary knowledge.Firstly, this paper introduces the basic principle of the Kelly formula in theory in the field of information transmission simple analogy investments to Kelly formula, introduces the Kelly formula of the origi-nal application. At the same time of elaborated the basic principle of the Kelly formula, Kelly is deduced in the application environment, the optimal investment proportion. Then introduces about the basic definition of the stochastic differential equation theory and application of some of the conclusions in this paper.The third chapter is the main research results in this paper. First of all, summa-rizes the preliminary knowledge of the general form of the Kelly formula application according to its general form compiled on the basis of stock investments yield. Second-ly introduced stock binary options, simply explain why binary options can be used in the Kelly formula. According to Black-Scholes model, defines binary options in math and binary option pricing formula is given. V(t,S)=e-T(T-t)N[d(t,S)], (2) Among them, V(t,S)Said for the price of the stock for S stock at t binary option σsaid underlying stock volatility, r said market interest rates, X said the exercise price of options, T said the validity of the option.Then, according to the definition and prior knowledge on the basis of stock invest-ments yield, introducing the idea of stochastic differential equation theory, calculated the binary options of profit and loss of probability and statistics yields of binary op-tions. Finally, according to the above results calculated based on the Kelly formula of binary options, the optimal investment proportion Among them x said standard normal distribution，Wti said 1 d Brownian motion, σsaid underlying stock volatility, r said market interest rates, t said the measurement of time.The fourth chapter carries on the summary and the outlook for paper.