A RBF based finite difference method for option pricing under regime-switching jump-diffusion model

Abstract

In this article, we presented a method for option pricing problem under regime-switching jump-diffusion models. We have proposed a numerical method for solving a partial integro-differential equation (PIDE) for pricing European option and for solving linear complementarity problem (LCP), to evaluate the price of American options. We use implicit explicit method for time semi discretization, followed by radial basis function based finite difference (RBF-FD) method for spatial discretization to solve PIDE. The proposed method is further extended to solve the LCP by coupling it with operator splitting method. Numerical simulation is done for European and American option to demonstrate efficiency and accuracy of the proposed method.     

泛逻辑学理论——机制主义人工智能理论的逻辑基础

当前，世界各主要大国都把人工智能作为它们的国家战略。人工智能的发展正在快速改变着人类的生活方式和思想观念。在中国，有一小批研究者20多年来一直在基于辩证唯物主义潜心研究具有普适性的人工智能基础理论，包括智能的形成机制、逻辑基础、数学基础、协调机理、矛盾转化等。终于，他们各自建立了机制主义人工智能理论、泛逻辑学理论、因素空间理论、协调学、可拓学、集对分析等。其中，机制主义人工智能理论是基于智能形成机制的通用理论，它能把现有的结构主义、功能主义和行为主义三大流派有机地统一起来，使意识、情感、理智成为三位一体的关系；因素空间理论是机制主义人工智能理论的数学基础；泛逻辑学理论是机制主义人工智能理论的逻辑基础。本文介绍了泛逻辑学理论的基本思想、理论基础和应用方法，阐明它的理论意义和应用价值。特别需要指出的是，在广义概率论基础上建立的命题泛逻辑（包括刚性逻辑和柔性逻辑），可看成一个完整的命题级智能信息处理算子库，库中完整地包含了全部18种柔性信息处理模式（包括16种布尔信息处理模式），可用类型编码<a,b,e>来严格区分，用它可寻找到适合自己的信息处理算子完整簇来使用。在每一个信息处理模式中，各种不确定性的组合状态由不确定性程度属性编码<k,h,β,e>来严格区分，用它可在本信息处理模式的算子完整簇中精确选择具体的算子来使用。这表明柔性信息处理本质上是一把密码锁，它需要专门的密码<a,b,e>+<k,h,β,e>才能正常打开，不能乱点鸳鸯谱。通过只有18种模式，每种模式可以从最大算子连续变化到最小算子，已经证明了没有一个命题算子被遗漏。     

增加[Δ]算子的Gödel[n]值命题逻辑系统理论的平均真度

在添加了[Δ]算子Gödeln值命题逻辑系统中，给出了Gödel[n]值命题逻辑系统中有限理论的平均真度的定义，给出了该系统下的一些重要结论并给予证明，验证了在该系统下平均真度的一些基本性质，为进一步在该系统下研究平均真度奠定了基础。     

Proximal extrapolated gradient methods for variational inequalities

The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also, the methods do not require Lipschitz continuity of the operator and the linesearch procedure uses only values of the operator. Moreover, when the operator is affine our linesearch becomes very simple, namely, it needs only simple vector–vector operations. For all our methods, we establish the ergodic convergence rate. In addition, we modify one of the proposed methods for the case of a composite minimization. Preliminary results from numerical experiments are quite promising.     

Stability analysis of PWM feedback control systems with PID regulators

Stability analysis is of great significance in those feedback control systems in which the power amplifier is operated as a pulse-modulator device, since under these circumstances the whole control system is highly non-linear. Stability in PWM feedback control systems with a proportional type regulator has been amply described in the literature. Only recently, however, have such studies been extended to include systems with a proportional-plus-integral regulator. In this paper the problem is considered for the case involving a PWM control system, where the regulator is a proportional-plus-integral-plus-derivative, the PWM modulator is of a very general type and the controlled process is of arbitrary order. The stability of the system is analysed by means of a discrete version of the second Lyapunov method ; this method in turn leads to an investigation of the positivity region of a quadratic form defined in the parameter space of the regulator. To improve the stability region obtained, a procedure is investigated whereby only a few parameters of the quadratic Lyapunov function need to be varied. The method proposed has proved extremely simple and flexible to apply, even in cases where the system is of arbitrary order.     

改进的Potrace提花织物图像矢量化算法

为了对提花织物图像进行矢量化,针对其颜色少、色块大的特点,提出了改进的Potrace图像矢量化算法。原始的Potrace算法只能实现对二值图像的矢量化,改进后的算法将位图中的色块逐个分解生成一个个的闭合路径,之后将这些闭合路径按照其各自分布拼接成树状结构并矢量化,最终生成一个完整的矢量图形。该算法在实际的应用中取得较好效果。     

Morphological enhancement of microscopy mineral image using opening‐ and closing‐based toggle operator

To enhance unclear microscopy mineral images, an algorithm based on toggle operator using opening and closing is proposed in this paper. Firstly, the specified toggle operator using opening and closing through designing the selection rules is analysed. Secondly, after importing the multiscale theory into the specified toggle operator, useful mineral image features, especially the mineral details, are extracted using the multiscale theory‐based toggle operator. Finally, the mineral image is enhanced through the strategy of enlarging the contrast between the extracted bright and dark image features. Experimental results on different types of mineral images verified that the proposed algorithm could effectively enhance mineral images and performed better than some other algorithms. The enhanced mineral image is clear and contains rich mineral details, whereas the grey scale distribution of the original mineral image is appropriately maintained. This would be useful for the further mineral analysis. Therefore, the proposed algorithm could be widely used for image‐based mineral applications.     

From distribution networks to smart distribution systems: Rethinking the regulation of European electricity DSOs

Distributed energy resources allow for new business models that have the potential to substantially change today's power system functioning paradigm. In particular, these changes pose challenges for distribution system operators (DSOs) and their regulation alike. This article sheds light on missing aspects in current regulation, recognizing DSOs as regulated monopolies, but also as key players along the supply chain. We provide insights on how regulation should be adjusted so that DSOs are incentivized to facilitate the market entry of welfare-enhancing technologies in a timely fashion, and to manage the distribution system efficiently in the presence of distributed energy resources.     

FUZZIFYING THE “PRECISE”

Based on the fuzzy-integral model, methods and algorithms are developed for identifying the “input–output” operator of continuous and stationary discrete extremal fuzzy dynamic systems (EFDS). The EFDS “input–output” operator is restored by means of experimental data with possibilistic uncertainty, the source of which is extremal fuzzy time intervals. The regularization conditions for obtaining quasi-optimal estimates are substantiated by the proved theorems. The corresponding algorithms are provided. The results obtained are illustrated by examples in the case of a finite set of EFDS states.