Options is an important part of global financial market，with great influence on national economies. While most classic option pricing models are based on the assumption of a constant interest rate, economic data show that interest rates in reality frequently fluctuated under the influence of varying economic performances and monetary policies. As interest rate fluctuation is closely related to the value and expected return of options, it is worth discussing option pricing under stochastic interest
rate models. Since 1990s, scholars home and abroad have been conducting researches on this topic and have formulated price formulas for some types of options. However, because the pricing process involves two stochastic variables, the majority of previous studies employed sophisticated methods. As a result, their price formulas were too complicated to provide straightforward explanations of the parameters’ influence on option prices, unable to offer investors direct assistance.
This paper selects Vasicek interest rate model to describe interest rate’s stochastic movement, and discusses the pricing of European equity options whose underlying asset’s price follows Geometric Brownian Motions in a complete market. The paper’s value and innovation lie in the following aspects: ① It improves and simplifies the pricing methods for options under stochastic interest rate models, applies comparatively primary mathematical methods, and attains concise price formulas; ② it
52 conducts in-depth analysis of major parameters’ financial significance, which helps investors to make better investment decisions by estimating the variations in option prices corresponding to different parameters.
Min ZhangStony Brook UniversityRen GuoOregon State UniveristyWei ZengSchool of Computing and Information Sciences, Florida International UniversityFeng LuoRutgers UniversityShing Tung YauHarvard UniversityXianfeng GuStony Brook Univerisity
Computational GeometryDifferential GeometryGeometric Modeling and ProcessingConvex and Discrete Geometry mathscidoc:1612.01001
Distinguished Paper Award in 2017
Graphical Models/Geometric Modeling and Processing 2014, 76, (5), 321-339, 2014.9
Ricci ﬂow deformsthe Riemannian metric proportionallyto the curvature, such that the curvatureevolves accordingto a heat diffusion process and eventually becomes constant everywhere. Ricci ﬂow has demonstrated its great potential by solving various problems in many ﬁelds, which can be hardly handled by alternative methods so far. This work introduces the uniﬁed theoretic framework for discrete Surface Ricci Flow, including all the common schemes: Tangential Circle Packing, Thurston’s Circle Packing, Inversive Distance Circle Packing and Discrete Yamabe Flow. Furthermore, this work also introduces a novel schemes, Virtual Radius Circle Packing and the Mixed Type schemes, under the uniﬁed framework. This work gives explicit geometric interpretation to the discrete Ricci energies for all the schemes with all back ground geometries, and the corresponding Hessian matrices. The uniﬁed frame work deepens our understanding to the the discrete surface Ricci ﬂow theory, and has inspired us to discover the new schemes, improved the ﬂexibility and robustness of the algorithms, greatly simpliﬁed the implementation and improved the efﬁciency. Experimental results show the uniﬁed surface Ricci ﬂow algorithms can handle general surfaces with different topologies, and is robust to meshes with different qualities, and is effective for solving real problems.
Pell equation is an important research object in elementary number theory of indefinite equation. its form is simple, but it is rich in nature. Many number theory problems can be transformed into the problem of Pell equation’s solvability. However, the previous methods in determining the Pell equation’s solvability are sophisticated for calculation, which leads to the lack of efficiency. This paper gives new and more widely used methods to determine the solvability of Pell equation, including several necessary conditions, sufficient conditions and necessary and sufficient conditions.
Yp Cao · Tao Ju · J Xu · Sm Hu. Extracting Sharp Features from RGB-D Images: RGB-D Sharp Features. 2016.
Shuai Zheng · Jun Hong · Kang Zhang · Baotong Li · Xin Li. A multi-frame graph matching algorithm for low-bandwidth RGB-D SLAM. In Computer-Aided Design.Volume 78.Page 107-117.2016.
Boyang Gao · Fei Chen · Franceso Trapani · Mario Selvaggio · Darwin G Caldwell. Robust object localization based on error patterns learning for dexterous mobile manipulation. In International Conference on Advanced Robotics and Mechatronics.Page 213-218.2016.
Lebeda K, Hadfield S, Bowden R.. TMAGIC: A model-free 3D tracker. In IEEE Transactions on Image Processing.2017.
Lebeda K.. 2D and 3D tracking and modelling. 2016.
Xiao Y, Feng C, Taguchi Y, et al.. User-Guided Dimensional Analysis of Indoor Building Environments from Single Frames of RGB-D Sensors. In Journal of Computing in Civil Engineering.Volume 31.Issue 4.2017.
Kim H, de Campos T, Hilton A.. Room Layout Estimation with Object and Material Attributes Information using a Spherical Camera. In International Conference on 3D Vision .Page 519-527.2016.
Cao Y P, Ju T, Xu J, et al.. Extracting Sharp Features from RGB‐D Images. In Computer Graphics Forum.
Cheng M M, Hou Q B, Zhang S H, et al. Intelligent Visual Media Processing: When Graphics Meets Vision. In Journal of Computer Science and Technology.Volume 32.Issue 1.Page 110-121.2017.
Yang S, Xu J, Chen K, et al.. View suggestion for interactive segmentation of indoor scenes. In Computational Visual Media.Page 1-16.2017.
3D scene modeling has long been a fundamental problem in computer graphics and computer vision. With the popularity of consumer-level RGB-D cameras, there is a growing interest in digitizing real-world indoor 3D scenes. However, modeling indoor
3D scenes remains a challenging problem because of the complex structure of interior objects and poor quality of RGB-D data acquired by consumer-level sensors. Various methods have been proposed to tackle these challenges. In this survey, we provide an overview of recent advances in indoor scene modeling techniques, as well as public datasets and code libraries which can facilitate experiments and evaluation.