Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1 ( simplifying as 'g-contraction mapping' ) has a...Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1 ( simplifying as 'g-contraction mapping' ) has a unique fixed point in M . Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.展开更多
Similar to the method of continuum mechanics, the variation of the price of index futures is viewed to be continuous and regular. According to the characteristic of index futures, a basic equation of price of index fu...Similar to the method of continuum mechanics, the variation of the price of index futures is viewed to be continuous and regular. According to the characteristic of index futures, a basic equation of price of index futures was established. It is a differential equation, its solution shows that the relation between time and price forms a logarithmic circle. If the time is thought of as the probability of its corresponding price, then such a relation is perfectly coincided with the main assumption of the famous formula of option pricing, based on statistical theory, established by Black and Scholes winner of 1997 Nobel' prize on economy. In that formula, the probability of price of basic assets (they stand for index futures here) is assummed to be a logarithmic normal distribution. This agreement shows that the same result may be obtained by two analytic methods with different bases. However, the result, given by assumption by Black-Scholes, is derived from the solution of the differential equation.展开更多
The basic equation of market price of option is formulated by taking assumptions based on the characteristics of option and similar method for formulating basic equations in solid mechanics: h 0(t)=m 1v -1 0(t...The basic equation of market price of option is formulated by taking assumptions based on the characteristics of option and similar method for formulating basic equations in solid mechanics: h 0(t)=m 1v -1 0(t)-n 1v 0(t)+F, where h,m 1,n 1,F are constants. The main assumptions are: the ups and downs of market price v 0(t) are determined by supply and demand of the market; the factors, such as the strike price, tenor, volatility, etc. that affect on v 0(t) are demonstrated by using proportion or inverse proportion relation; opposite rules are used for purchasing and selling respectively. The solutions of the basic equation under various conditions are found and are compared with the solution v f(t) of the basic equation of market price of futures. Furthermore the one_one correspondence between v f and v 0(t) is proved by implicit function theorem, which forms the theoretic base for study of v f affecting on the market price of option v 0(t).展开更多
文摘Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1 ( simplifying as 'g-contraction mapping' ) has a unique fixed point in M . Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.
文摘Similar to the method of continuum mechanics, the variation of the price of index futures is viewed to be continuous and regular. According to the characteristic of index futures, a basic equation of price of index futures was established. It is a differential equation, its solution shows that the relation between time and price forms a logarithmic circle. If the time is thought of as the probability of its corresponding price, then such a relation is perfectly coincided with the main assumption of the famous formula of option pricing, based on statistical theory, established by Black and Scholes winner of 1997 Nobel' prize on economy. In that formula, the probability of price of basic assets (they stand for index futures here) is assummed to be a logarithmic normal distribution. This agreement shows that the same result may be obtained by two analytic methods with different bases. However, the result, given by assumption by Black-Scholes, is derived from the solution of the differential equation.
文摘The basic equation of market price of option is formulated by taking assumptions based on the characteristics of option and similar method for formulating basic equations in solid mechanics: h 0(t)=m 1v -1 0(t)-n 1v 0(t)+F, where h,m 1,n 1,F are constants. The main assumptions are: the ups and downs of market price v 0(t) are determined by supply and demand of the market; the factors, such as the strike price, tenor, volatility, etc. that affect on v 0(t) are demonstrated by using proportion or inverse proportion relation; opposite rules are used for purchasing and selling respectively. The solutions of the basic equation under various conditions are found and are compared with the solution v f(t) of the basic equation of market price of futures. Furthermore the one_one correspondence between v f and v 0(t) is proved by implicit function theorem, which forms the theoretic base for study of v f affecting on the market price of option v 0(t).
