Confidence-based optimisation for the newsvendor problem under binomial,Poisson and exponential demand

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach produces an upper and a lower bound for the associated cost. We apply this approach to three demand distributions in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist—e.g. based on maximum likelihood estimators—or Bayesian strategies.     

A semilocal convergence result for Newton’s method under generalized conditions of Kantorovich

From Kantorovich’s theory we establish a general semilocal convergence result for Newton’s method based fundamentally on a generalization required to the second derivative of the operator involved. As a consequence, we obtain a modification of the domain of starting points for Newton’s method and improve the a priori error estimates. Finally, we illustrate our study with an application to a special case of conservative problems.     

基于傅立叶变换的SVJ模型的欧式期权定价

为了更加精确的计算期权价格,将结合随机波动和跳扩散模型(以下简称SVJ模型)以更好的描述期权标的资产价格过程,然而这样的价格过程无法得到概率密度函数的封闭形式,而只能得到包含特殊函数和无限求和的复杂的表达式.不过它们的特征函数都是封闭且是唯一的,因而可以通过它们的特征函数,并运用两种傅立叶变换的方法来求出期权价格.其中FFT算法计算的结果将与Monte Carlo模拟得出的结果进行比较,然后再将SVJ模型的计算结果和Black-Scholes模型进行比较.     

Laplacian型算子三点边值问题正解的存在性

利用Krasnoselskii不动点定理,研究了带Lalacian型算子的三点边值问题正解的存在性,得到其存在正解的充分条件,改进和丰富了以往文献的一些结论.     

具p-Laplace算子的分数阶微分方程边值问题的正解

考虑具有p-Laplace算子的分数阶泛函微分方程边值问题,利用锥上的不动点定理,得到了其正解及多个正解存在的充分条件,所得结果推广了已有的结论,并举例说明了结论的适用性.     

Superconvergence analysis of fully discrete finite element methods for semilinear parabolic optimal control problems

We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization is based on difference methods, whereas the space discretization is done using finite element methods. The state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions. First, we define a fully discrete finite element approximation scheme for the semilinear parabolic control problem. Second, we derive the superconvergence properties for the control, the state and the adjoint state. Finally, we do some numerical experiments for illustrating our theoretical results.     

非线性边值条件非线性方程的奇摄动问题

研究了三阶非线性边值条件的非线性方程奇摄动问题,先用合成展开法对形式近似解进行构造,再利用相关微分不等式理论给出所得解的存在性及一致有效性的证明.     

具有Hille-Yosida算子的非线性随机脉冲泛函微分包含的可控性

本文研究具有Hille-Yosida算子的非线性随机脉冲泛函微分包含的可控性.假设多值非线性和脉冲函数满足由非紧性测度表示的正则性条件,利用非紧性测度理论和多值凝聚不动点定理,得到这类微分包含的可控性的充分条件.     

关于有限族Lipschitz映射多步Ishikawa迭代算法的收敛性及其应用

本文的目的是研究Lipschitz映射公共不动点问题.基于传统的Ishikawa迭代和Noor迭代方法,我们引入多步Ishikawa迭代算法,并且分别给出了该算法强收敛于有限族拟-Lipschitz映射和伪压缩映射公共不动点的充分必要条件.此外,我们证明了该算法强收敛到非扩张映射的公共不动点.作为应用,我们给出数值试验证实所得的结论.     

求解非线性互补问题的一类光滑Broyden-like方法

非线性互补问题可以等价地转换为光滑方程组来求解. 基于一种新的非单调线搜索准则, 提出了求解非线性互补问题等价光滑方程组的一类新的非单调光滑 Broyden-like 算法.在适当的假设条件下, 证明了该算法的全局收敛性与局部超线性收敛性. 数值实验表明所提出的算法是有效的.