随机Benjamin-Ono 方程初值问题及对河口区域生物分布的应用

该文对具梯度耦合噪声的随机Benjamin-Ono 方程（以下简记为B-O方程）的初值问题导出了解得积分表达式，并将它应用于河口区域生物分布问题，得到了一维空间的分布表达式。     

欧氏空间上的随机覆盖及其应用

运用Borel—Cantelli引理，改进并推广了Jean-Pierre Kahane在单位圆周上关于随机覆盖的结果，得到了在高维欧氏空间上关于随机覆盖的类似结果。且运用这些结果研究了多指标复Fourier-Redemacher级数与某些函数空间的关系，得到了多指标复Fourier—Redemacher级数几乎处处属于L^∞及几乎处处属于C的等价性。     

制造模式变迁的动力机制及其特征分析

制造模式变迁过程受制于三类因素，即制造模式现有状态、制造模式的四大基本维度（技术与方法、文化、组织结构以及和谐管理)和外部环境中的随机涨落因素。该过程表现出非平衡相变、对称性破缺、分叉等特征。当新的制造模式形成时，其研发投入、文化、组织结构及其管理、知识调配都须有很大的变动和调整。     

动态随机弹性在期权定价中的应用

给出动态随机弹性的概念及运算性质,讨论了动态随机弹性在期权定价模型中的应用.主要结果有:(1)在波动率为常数时,期权价格对的弹性,得到了动态随机弹性服从运动,并给出了相应的经济解释;(2)由于波动率一般不是常数,也是随机过程,因此本文进一步研究了期权价格对波动率的弹性,就股票价格的波动情况给出了数学描述和金融意义上的解释.     

Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance.     

Second order Runge–Kutta methods for Stratonovich stochastic differential equations

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly. AMS subject classification (2000)  65C30, 65L06, 60H35, 60H10     

A Partial Differential Inequality in Geological Models

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation.This limiter happens to satisfy a stationary scalar hyperbolic inequality,within a constraint,for which the authors prove the existence and the uniqueness of the solution.Actually,this solution is shown to be the maximal element of a convenient convex set of functions.The existence proof is obtained thanks to the use of a numerical scheme.     

Practical aspects associated with location planning for maternal and perinatal assistance in Brazil

A study has been carried out aimed at reducing perinatal mortality in the municipality of Rio de Janeiro through a better distribution of health care facilities. The algorithmic aspects are detailed elsewhere and here the emphasis is on practical issues and difficulties encountered. A 3-level hierarchical model was developed. Both uncapacitated and capacitated versions are briefly described together with some results based on actual data. The project brought to light many contradictions between OR theory and practice in developing countries and, unfortunately, the models developed were not implemented by the municipality health authorities. Possible reasons for this outcome are analysed.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.