Random simulation of population growth, random simulation of circuits, filtering problems, optimal stopping time and optimal investment portfolio, these seemingly unrelated problems can't be linked at all in the eyes of ordinary people, but when the mathematical equations are written on the blackboard, Teacher Fan Zhencheng connects these five problems in series with stochastic differential equations, which is exactly what Teacher Fan Zhencheng wants to explain.
? On February 26th 10 1, the 17th lecture in the series of "Professor Lecture Hall" was held in Building B of the Engineering Building. Teacher Fan Zhencheng from the Department of Mathematics of Minjiang University, as the keynote speaker, took us into the world of stochastic differential equations.
In this lecture, Teacher Fan introduced stochastic differential equations and their applications in some important fields. Fan Zhencheng, Ph.D., Professor of Mathematics Department of Minjiang University, majoring in "? Numerical solutions of stochastic differential equations ". In the diary? Yes? Math? Analysis? And then what? Application, Journal? Yes? Calculation? Application? Mathematics, Application? Value? Mathematics, Application? Math? And then what? He has published more than ten academic papers in Computation, Computational Mathematics and Journal of Applied Mathematics. Completed 3 provincial-level projects such as Fujian Natural Science Foundation. He has taught professional courses such as numerical calculation method, probability theory and ordinary differential equations. In the lecture, after enumerating and explaining five problems: stochastic simulation of population growth, stochastic simulation of circuit, filtering problem, optimal stopping time and optimal portfolio, Teacher Fan said, "Stochastic differential equations are widely used in production and life, especially in the financial field." Teacher Fan's courseware and differential equations involve a key word "noise". Teacher Fan explained to the students present: "From a mathematical point of view, the noise at every moment is a random variable, which may be different at different times, so the noise in a period of time should be regarded as a random process, and this" noise "is one of the most important factors in stochastic differential equations."
"Noise" is closely related to Brownian motion. "British botanist robert brown discovered this phenomenon when observing pollen suspended in water, and later researchers called this phenomenon Brownian motion; Einstein and Wiener gave the mathematical explanation of Brownian motion. Teacher Fan introduced the original source and development process of stochastic differential equations, which made the students here have a deeper understanding of stochastic differential equations. After that, Teacher Fan focused on the related applications of Ito formula and other related equations, from related calculus to practical application, and explained them in great detail. At the application level, Teacher Fan listed the importance and practical significance of stochastic differential equations mainly from the options in the financial field. " European call option is a kind of financial contract, and the contract holder has the right but no obligation to buy stock S at the price P at time T … "Teacher Fan used stochastic differential equation to analyze the variables and process of stock purchase.
Because it is too professional, Teacher Fan briefly introduced arbitrage and hedging. "The key issue of option pricing is arbitrage, that is, risk-free profit. In practical application, the problem of option pricing is transformed into the solution of partial differential equation by using this principle, and some conditions can also find the boundary conditions of option pricing for us. Option pricing is a very important issue, and the option pricing formula also solves the option pricing problem. " Through examples, the students here also made clear the option pricing problem and the application of related equations.
Benefit a lot
Mathematics involves all aspects of life, from the national economy to family expenses. Teacher Fan's wonderful explanation made more students understand that mathematics is a very important tool and means, and the application of mathematics is also a very common phenomenon. ? "Through this lesson, I learned the basic functions, basic calculation methods and specific applications of stochastic differential equations. I didn't like this complicated calculation equation before, but now I think it's quite interesting.
17 chemical engineering department said after class. ? "Because we have never been exposed to stochastic differential before, this class taught me what stochastic differential is, how to calculate it, what knowledge we can use to solve it and where it can be applied." Wu Tianfeng, a student from the Department of Chemical Engineering 17, said after Teacher Fan's lecture that he had a better understanding of stochastic differential equations.