Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem

This paper concerns optimal investment problem of a CRRA investor who faces proportional transaction costs and finite time horizon. From the angle of stochastic control, it is a singular control problem, whose value function is governed by a time-dependent HJB equation with gradient constraints. We reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. This enables us to make use of the well-developed theory of obstacle problem to attack the problem. The C2,1 regularity of the value function is proven and the behaviors of the free boundaries are completely characterized.     

Convergence results for obstacle problems on metric spaces

Let X be a complete metric space equipped with a doubling Borel measure supporting a p-Poincaré inequality. We obtain various convergence results for the single and double obstacle problems on open subsets of X. In particular, we consider single and double obstacle problems with fixed obstacles and boundary data on an increasing sequence of open sets.     

A numerical approach to the proof of existence of solutions for some generalized obstacle problems

In [8], we proposed some numerical verification methods for automatic proof of the existence of solution for obstacle problems. In this paper we propose a new iterative algorithm to automatically prove the existence of solutions for some generalized obstacle problems.     

LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS

We obtain a local regularity result for solutions to Kψ,θ-obstacle problem of A-harmonic equation divA(x,u(x),▽u(x))=0,where A:Ω× R×Rn → Rn is a Carath'eodory function satisfying some coercivity and growth conditions with the natural exponent 1pn,the obstacle function ψ≥0,and the boundary data θ∈W1,p(?).     

Metaphor or Met-Before? The effects of previouos experience on practice and theory of learning mathematics

While the general notion of ‘metaphor’ may offer a thoughtful analysis of the nature of mathematical thinking, this paper suggests that it is even more important to take into account the particular mental structures available to the individual that have been built from experience that the individual has ‘met-before.’ The notion of ‘met-before’ offers not only a principle to analyse the changing meanings in mathematics and the difficulties faced by the learner—which we illustrate by the problematic case of the minus sign—it can also be used to analyse the met-befores of mathematicians, mathematics educators and those who develop theories of learning to reveal implicit assumptions that support our thinking in some ways and act as impediments in others.     

Global higher integrability of solutions to subelliptic double obstacle problems

In this paper we consider the double obstacle problems associated with nonlinear subelliptic equation \[X^*A(x,u,Xu)+ B(x,u,Xu)=0, \ \ x\in\Omega,\] where $X=(X_1,\ldots,X_m)$ is a system of smooth vector fields defined in $\mathbb{R}^n$ satisfying H\"{o}rmander"s condition. The global higher integrability for the gradients of the solutions is obtained under a capacitary assumption on the complement of the domain $\Omega$.     

适用于实时避障的新型智能化机器人敏感皮肤的研究

在未知环境中,实时避障是实现智能化机器人自主工作的关键技术。敏感的皮肤可以使智能机器人具有环境感知和实时决策的能力。研制的敏感皮肤南模块化和带有强数据处理能力的微型红外传感器阵列构成,可以粘贴在机器人表面,依赖于皮肤上的红外传感器来感知外部环境。系统采用了几何光学模型法来测量敏感皮肤与障碍物间的距离。实验结果表明,在感知区域内,敏感皮肤能够实时准确地给出多关节机器人周围的障碍物存在和距离信息,为解决机器人避障问题提供新的范例。同时敏感皮肤的研制也是机器人在传感和控制领域中应用的一次尝试,对促进机器人和各相关科学的发展及提高机器人智能化的水平具有深远的意义,并将有着广阔的应用前景。     

单障碍问题区域分解法的单调收敛性与收敛速度估计

本文我们考虑一类典型的椭圆型算子的障碍问题的区域分解算法,分析算法的单调收敛性并给出相应的收敛速度估计.障碍问题有着重要的物理背景（参见[3,9]）.近些年来,有关障碍问题的区域分解法方面的研究已经有一些成果.关于线性算子情形,读者可参看[1,2,5,7,8,10,12,13,14,15,17]等文献,而对于非线性算子情形,读者可参看[4,6,16,18].在这些文献中,已经有部分涉及到算法的收敛速度估计.例如,文[15,16]给出了有限元区域分解算法的迭代误差的渐近最大模估计,文[13]给出了求解具M-阵的有限维互补问题     

Finite-Difference Method for a System of Third-Order Boundary-Value Problems

In this paper, we develop a two-stage numerical method for computing the approximate solutions of third-order boundary-value problems associated with odd-order obstacle problems. We show that the present method is of order two. A numerical example is presented to illustrate the applicability of the new method. A comparison is also given with previously known results.     

Polynomially bounded algorithms for locatingp-centers on a tree

We discuss several forms of thep-center location problems on an undirected tree network. Our approach is based on utilizing results for rigid circuit graphs to obtain polynomial algorithms for solving the model. Duality theory on perfect graphs is used to define and solve the dual location model.