On the asymptotic free boundary for the American put option problem

In practical work with American put options, it is important to be able to know when to exercise the option, and when not to do so. In computer simulation based on the standard theory of geometric Brownian motion for simulating stock price movements, this problem is fairly easy to handle for options with a short lifespan, by analyzing binomial trees. It is considerably more challenging to make the decision for American put options with long lifespan. In order to provide a satisfactory analysis, we look at the corresponding free boundary problem, and show that the free boundary—which is the curve that separates the two decisions, to exercise or not to—has an asymptotic expansion, where the coefficient of the main term is expressed as an integral in terms of the free boundary. This raises the perspective that one could use numerical simulation to approximate the integral and thus get an effective way to make correct decisions for long life options.     

基于信息融合技术的多传感器智能轮椅避障系统

在智能轮椅障碍物探测中,需要实时准确地感知环境信息,而单一传感器仅能提供部分环境信息,对环境进行描述时存在局限。提出采用激光传感器和超声波传感器相结合来感知外界环境信息,设计了激光传感器数据采集和基于单片机控制的8路超声波探测系统的软件和硬件,利用自适应加权融合算法实现数据融合较好地满足了智能轮椅障碍探测的需要,具有一定的有效性和实用性。     

Random Homogenization of p-Laplacian with Obstacles in Perforated Domain

We study the homogenization of p-Laplacian with obstacles in perforated domain, where the holes are periodically distributed and have random size. And we assume that the p-capacity of each hole is stationary ergodic.     

The Caffarelli Alternative in Measure for the Nondivergence Form Elliptic Obstacle Problem with Principal Coefficients in VMO

We study the obstacle problem with an elliptic operator in nondivergence form with principal coefficients in VMO. We develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results, in turn, allow us to begin the study of the regularity of the free boundary, and we show existence of blowup limits, a basic measure stability result, and a measure-theoretic version of the Caffarelli alternative proven in [3 Caffarelli , L.A. ( 1977 ). The regularity of free boundaries in higher dimensions . Acta Math. 139 : 155 – 184 .[Crossref], [Web of Science ®] , [Google Scholar]].     

Sous ellipticite dans le cadre du calcul S(m,g)

Abstract

We study the regularity of the free boundary in the two membranes problem. We prove that around any point the free boundary is either a C ^{1, α} surface or a cusp, as in the obstacle problem. We also prove C ^{1, 1} regularity for the pair of functions solving the problem.     

Local existence of energy class solutions for the dirac—klein—gordon equations

Abstract

We show a method to eliminate a type of mixed asymptotics in certain free boundary problems, and give two examples of its application. It appears that these problems cannot be handled by the monotonicity formula of Alt et al. [Alt, H. W., Caffarelli, L. A., Friedman, A. (1984). Variational problems with two phases and their free boundaries. Trans. Am. Math. Soc. 282(2):431–461] or by the more recent monotonicity formula of Caffarelli et al. [Caffarelli, L. A., Jerison, D., Kenig, C. E. (2002). Some new monotonicity theorems with applications to free boundary problems. Ann. Math. (2) 155(2):369–404].     

基于人工势场法的无人机路径规划避障算法

随着无人机广泛应用于生产生活的各个方面,无人机的避障研究成为热点问题。为了提高无人机的避障性能,文中提出一种基于人工势场法的无人机路径规划避障算法。该算法通过生成预规划路径弱化了目标点对无人机的吸引作用,增加了路径的连贯性;在势场函数中加入了动态调节因子,可减少无人机轨迹不必要的转弯机动,减少机动能耗;该算法综合考虑无人机飞行中的安全性、平滑性和机动能耗,提出了一种新的代价函数,并通过使得代价函数最小化来选出最优路径。实验结果表明,该算法克服了传统人工势场的不足,在不同的飞行环境下均能够规划出安全、平滑、机动能耗小的路径,有效避开障碍物,且具有较好的适应性。