非线性金融模型与金融计算的复杂性

The nonlinearity, complexity ，the simulation and the optimization.algorithms of finance systems are studied in this project systematically and quantitatively. The mathematical models for stocks,futures, interest rate, exchange rate and their derivatives are established and improved through stochastic analysis, stochastic differential equation, nonlinear science, statistics and numerical analysis. The strong calculability of a large class of finance calculating problems is proved. The complexity is reduced by the.variance reduction technique, Markov Monte Carlo and Quasi Monte Carlo.methods, and its accuracy is improved. The Bayesian network method is.used in data mining. A Markov decision model of the investment and.investment-consumption is interpreted as the risk model and an iterated approximation algorithm for the optimum strategy is obtained.

该项目将对金融系统的复杂性进行定量研究。利用随机分析、随机微分方程、非线性科学、统计学和计算方法，建立并完善股票、期货、利率和汇率及其衍生物的新的数学模型，研究金融系统中的非线性机制。同时，致力于金融计算及其复杂性研究。结合中国的实际进行金融风险预测分析。本项目具有重要的理论与实用价值。