Error analysis of finite difference and Markov chain approximations for option pricing

Mijatovi? and Pistorius proposed an efficient Markov chain approximation method for pricing European and barrier options in general one‐dimensional Markovian models. However, sharp convergence rates of this method for realistic financial payoffs, which are nonsmooth, are rarely available. In this paper, we solve this problem for general one‐dimensional diffusion models, which play a fundamental role in financial applications. For such models, the Markov chain approximation method is equivalent to the method of lines using the central difference. Our analysis is based on the spectral representation of the exact solution and the approximate solution. By establishing the convergence rate for the eigenvalues and the eigenfunctions, we obtain sharp convergence rates for the transition density and the price of options with nonsmooth payoffs. In particular, we show that for call‐/put‐type payoffs, convergence is second order, while for digital‐type payoffs, convergence is generally only first order. Furthermore, we provide theoretical justification for two well‐known smoothing techniques that can restore second‐order convergence for digital‐type payoffs and explain oscillations observed in the convergence for options with nonsmooth payoffs. As an extension, we also establish sharp convergence rates for European options for a rich class of Markovian jump models constructed from diffusions via subordination. The theoretical estimates are confirmed using numerical examples.     

基于数字图像处理技术的再生混凝土数值模拟

为了研究骨料形态对再生混凝土材料力学性能的影响,基于势能原理的基面力元法,利用图像处理技术和MATLAB软件,建立了再生混凝土真实骨料细观模型。应用FORTRAN分析软件对再生混凝土试件进行单轴拉伸试验的数值模拟,研究了真实骨料细观模型再生混凝土宏观应力-应变曲线变化规律和试件的破坏形态。结果显示,真实骨料模型得到的宏观应力-应变曲线和试验曲线吻合度较高,骨料形状对试件的破坏形态影响较小。模型可真实地模拟再生混凝土在单轴拉伸作用下的损伤破坏过程,准确地反映试件的实际骨料形态。     

多孔连续斜交框架桥顶进施工过程受力分析

城市道路下穿铁路框架桥顶进施工的关键是合理控制桥梁主体结构的受力。为了对框架桥顶进施工过程进行受力特性分析，采用Midas有限元软件模拟了框架桥在滑板上开始顶进、框架桥重心即将离开滑板、框架桥顶进即将就位三个施工阶段。结果表明，该框架桥的施工过程是安全可靠的，同时结合工程项目实际给出了顶进施工的注意事项。该方法可用来指导类似工程顶进施工过程的受力分析和施工控制。     

略论应将人列入景观及景观设计之要素

在通常的风景园林书籍中，未曾明确将人及其活动列入景观设计的要素。喜欢观看他人及被人观看是人的本性之一。明确提出并论述应将人及其活动列入景观及景观设计之要素的必要性。在风景园林等景观场所的规划设计中，将人及其活动作为景观要素之一加以考虑，必将进一步拓宽景观规划设计的视野，增加其维度，有助于提升景观设计的水平，使所设计的景观更加人性化，更加体现以人为本的理念，为建设美丽中国，留住乡愁作出贡献。     

Research on a diagnostic system of rural vitalization based on development elements in China

In 2017, the Chinese government implemented a national strategy of "Rural Vitalization" that sought to realize full-scale rural vitalization. However, is it possible to achieve vitalization for all the villages in China? How should their development potential be determined? This paper identified and analyzed the "element-composite" messages of rural development based on 99 exemplary sites of “Beautiful Villages” in China. Combined with the projection pursuit classification method, a diagnostic system of rural vitalization was established; then, Dehua County was taken as a case study for an in-depth analysis. Based on national data analysis, the final results indicated that livelihood resources (LR), agglomeration effects (AE), location and transportation (LT), cultural/natural landscapes (CN), and economic circumstance (EC) are essential elements for successful rural development. Additionally, EC was the only exogenous element, while the remaining elements were endogenous. Furthermore, the villages with better EC presented urbanization rates of 38∼82 % and Engel coefficients of 29∼41 % in their counties; exemplary sites lacking LR, CN, LT, and AE account for 13.13 %, 19.19 %, 26.26 %, and 60.61 % respectively, so the indispensability of these elements decreases progressively in sequence. Only 2 % of villages rely on single element for success, therefore, the composite pattern of development element was also critical; 10 out of 16 types were found to successfully facilitate village development, among which, the type of R-a-L-C (32.32 %) and R-A-L-C (15.15 %) were considered as the greatest potential patterns for vitalization. Finally, by means of the diagnostic system, the ratio of representative villages for high-low potential in Dehua County is evenly split; then, development paths, and land use policies that match with paths were proposed, on the basis of development potential and “element-composite” condition of themselves.     

主题乐园长盛不衰十大要素论析——以美国迪斯尼世界为案例的实证研究

主题乐园是当今流行的娱乐旅游方式.本文以美国奥兰多迪斯尼世界为例进行了全面的研究,总结了主题乐园长盛不衰的10大要素.它们分别是:土地,选址,定位,消费能力,房产联动,融资,高新科技的坚实后盾,活动节目综合多样,动态与参与,服务.作者根据中国国情提出了对此借鉴、学习、创新和引进的思路.     

栈桥钢管桩浮冰冲击作用下的有限元分析

本文运用有限元分析软件Midas civil和ANSYS分别建立了栈桥钢管桩的整体及局部有限元模型,分析了在浮冰冲击荷载作用下钢管柱的受力情况,为栈桥检算提供理论依据,同时优化设计方案,保证了栈桥在使用中的安全可靠。     

股权激励效应研究述评与展望

股权激励效应一直是学界研究和探讨的焦点,但却始终没能达成一致的研究结论。经过系统回顾股权激励领域的相关理论观点和经验研究,发现股权激励效应的研究存在契约整体观、契约要素观和契约结构观三种研究思路。文章以股权激励效应研究思路的演进路径为主线,对三种思路下的研究成果进行了阐释和述评,并展望了今后的研究方向和关键问题。     

预紧力对接触网套管双耳强度的影响分析

本文以失效频率很高的接触网零部件套管双耳作为研究对象,简化其力学模型,考虑预紧力、风载、履冰三种载荷因素对套管双耳最大的应力影响。根据实际情况,分12种工况对接触网套管双耳进行数值模拟。研究结果表明,预紧力对套管双耳强度影响较为显著,在实际安装中以2500N为宜。为接触网套管双耳的静强度可靠性研究和设计提供了参考。     

关于几类典型的定积分的计算方法

本文通过具体例题,介绍了几类典型的定积分计算的方法,掌握这些方法和技巧既可减少计算量,提高效率,又可以开拓解题思路,提高定积分的解题技能。同时给出了概率积分+∞0乙e-x2dx一种最简单的计算方法。