静态输出反馈的鲁棒H_∞控制的一种代数方法

对于一类线性连续不确定性系统,基于线性代数的方法,研究了静态输出反馈控制的鲁棒H_∞问题.结果显示:静态输出反馈控制的鲁棒问题的可解性等价于两个修正Riccati的不等式有正定解,并且给出了符合设计要求的允许控制器的解析表达式.     

国际投资商组合投资决策模型研究(英文)

在国际金融市场上,投资商参与风险资产投资,国际投资商的投资行为不仅受风险资产价格变动的影响,而且受外汇市场汇率波动风险的影响,在投资者效用最大化的标准下,本文研究了国际金融市场的投资者投资决策模型．在确定性系数下,提供了反馈形式的消费投资公式,并就股价或汇率变动对投资者行为的影响进行了理论分析．分析表明,我们的模型从理论上可以解释１９９７ 年以东南亚为起点的金融危机对国际资本流动的影响     

Convex Duality in Portfolio Optimization under Constraints and with Higher Interest Rate for Borrowing

We study the stochastic control problem of maximizing expected utility from terminal wealth and/or consumption, when the portfolio is constrained to take values in a given closed, convex subset of Rd, and in the presence of a higher interest rate for borrowing. The setting is that of a continuous-time, Ito process model for the underlying asset prices. The solution of the unconstrained problem is given. In addition to the original constrained optimization problem, a so-called combined dual problem is introduced. Finally, the existence question of optimal processes for both the dual and the primal problem is settled.     

不允许借款同时不允许卖空情况下期权的定价

分析了金融期权的定价,讨论了在不允许借款购买股票同时不允许卖空约束下期权的定价及投资策略.     

正倒向随机微分方程解的比较定理

讨论了正倒向随机微分方程解的比较问题.阐述了正倒向随机微分方程在随机最优控制、现代金融理论中的广泛而深刻的应用, 对于一类正倒向随机微分方程, 利用Ito公式、停时等随机分析方法,通过构造辅助正倒向随机微分方程,得到了正倒向随机微分方程解的比较定理.     

MATHEMATICAL MODELS OF MACROMOLECULAR CONFORMATIONS AND THEIR APPLICATION

In this paper we suggest that the mathematical model of 6-dimensional (or more generally, n-dimensional) Brownian motion can be used to simulate the conformations of a macromolecular chain with the short (or long) range interaction. The dimensional value n is a significant characteristic of the flexibility-stiffness of the polymer chain. Under the condition of the constant module of the end-to-end state vector, we derived the probabilistic expression for the continuous transition of polymer chains from flexibility to stiffness.These models are still valid if the excluded volume effect is considered. By using the concept of the first hitting-time, we obtained the analytical expression of the partial transfer probability density function q_B(n,x;y) and the formula for calculating the parameter of the excluded volume effect.     

Convergence Theorems for Fuzzy Superpramarts

The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided.Finally, the graph Kuratowski-Mosco convergence and D-convergence of fuzzy (super) pramart and quasi-martingale are studied.     

STUDY ON THE THEORY OF S.D.E.AND ITS APPLICATION IN ECONOMIC MODELLING(Ⅱ)

A general consumption/investment problem have been considered for an agent whose actions cannot affect the market prices, and strive to maximize total expected discounted utility of both consumption and terminal wealth . Furthermore, Karatzas et al. has also approached the case of market model with constant coefficients. We have generalized the model with constant coefficients to more general case[2] , where we supposed discount process β( t) to be finite piecevrise function. We will further generalize our previous results when β( t) is infinite piecewise and continuous functions, respectively.     

随机微分方程理论在经济建模中的应用研究

考虑投资者参与证券投资及消费．由于证券、价格的变动趋势受诸多因素的影响，显示出价格很不稳定．用随机微分方程来刻划证券价格的变动趋势是合理的．Ｋａｒａｔｚａｓ等人在［１］中研究了最优消费与投资的一般特性，而且在模型参数为常系数假设下给出了反馈形式的最优消费与投资公式．但模型系数都为常值的假设在实际应用中显然有很大的局限性．为此，本文就β（ｔ）为有限分段函数情形推广了Ｋａｒａｔｚａｓ等人的结果．所得结论比Ｋａｒａｔｚａｓ［１］所得结论更具有应用价值．     

共轭凸轮研究——求共轭双凸轮廓线方程的几种数学方法以及压力角的计算

本文研究了求共轭双凸轮廓线的一些方法,并发现了它们之间的内在联系,顺便消除了有些文献中的不当之处,用数学推导完整了这方面的理论.此外,文中还求得了压力角的变化规律的一般公式,为设计最理想的凸轮提供了理论依据,采用这种方法不仅可消除冲击和减小噪声,而且为设计与加工自动化奠定了基础.