Conditional expectation determination based on the J-process using Malliavin calculus applied to pricing American options

The aim of our paper is to elaborate a theoretical methodology based on the Malliavin calculus to calculate the following conditional expectation (P_t(X_t)|(X_s)) for s≤t where the only state variable follows a J-process [Jerbi Y. A new closed-form solution as an extension of the Black—Scholes formula allowing smile curve plotting. Quant Finance. 2013; Online First Article. doi:10.1080/14697688.2012.762458]. The theoretical results are applied to the American option pricing, consisting of an extension of the work of Bally et al. [Pricing and hedging American options by Monte Carlo methods using a Malliavin calculus approach. Monte Carlo Methods Appl. 2005;11-2:97–133], as well as the J-process (with additional parameters λ and θ) is an extension of the Wiener process. The introduction of the aforesaid parameters induces skewness and kurtosis effects, i.e. smile curve allowing to fit with the reality of financial market. In his work Jerbi [Jerbi Y. A new closed-form solution as an extension of the Black–-Scholes formula allowing smile curve plotting. Quant Finance. 2013; Online First Article. doi:10.1080/14697688.2012.762458] showed that the use of the J-process is equivalent to the use of a stochastic volatility model based on the Wiener process as in Heston's. The present work consists on extending this result to the American options. We studied the influence of the parameters λ and θ on the American option price and we find empirical results fitting with the options theory.     

The Microeconomics of Efficient Group Behavior: Identification1

Consider a group consisting of S members facing a common budget constraint p'ξ=1: any demand vector belonging to the budget set can be (privately or publicly) consumed by the members. Although the intragroup decision process is not known, it is assumed to generate Pareto‐efficient outcomes; neither individual consumptions nor intragroup transfers are observable. The paper analyzes when, to what extent, and under which conditions it is possible to recover the underlying structure—individual preferences and the decision process—from the group's aggregate behavior. We show that the general version of the model is not identified. However, a simple exclusion assumption (whereby each member does not consume at least one good) is sufficient to guarantee generic identifiability of the welfare‐relevant structural concepts.     

从辩证逻辑视角看微积分

在当今科学哲学界,虽然辩证法派属于少数派,但作者却愿意加入这一行列。作者立足于数学上公认的事实材料,用辩证逻辑的流动范畴的眼光来分析微积分主要的基本概念的辩证本性,并且对微积分与代数、代数与算术之间的关系,和辩证逻辑与形式逻辑之间的关系,进行对应与类比,从而在辩证思维的语境中揭示了数学中所隐含的辩证逻辑内涵。     

Optimal Berry–Esseen bound for parameter estimation of SPDE with small noise

We investigate a rate of convergence on asymptotic normality of the maximum likelihood estimator (MLE) for parameter $\theta$ appearing in parabolic SPDEs of the form

$d{u}^{?}(t,x)=(A_0+\theta A_1)u^{?}(t,x)dt+?dW(t,x),$

where $A_0$ and$A_1$ are partial differential operators, $W$ is a cylindrical Brownian motion (CBM) and $?\downarrow 0$. We find an optimal Berry–Esseen bound for central limit theorem (CLT) of the MLE. It is proved by developing techniques based on combining Malliavin calculus and Stein’s method.     

辩证法在微积分中的体现

辩证法是科学的世界观和方法论,微积分中则充满了辩证法,体现了辩证法对立统一规律、质量互变规律、否定之否定规律。在微积分的创立和发展中、微积分的基本概念中和微积分的基本思想中,蕴含了丰富的辩证法。了解微积分这一数学工具对于加深理解辩证法思想有现实的帮助,本文试图探析辩证法在微积分中的体现,以期达到更深理解辩证法的目的。     

非周期TBox框架下的推理——拟经典描述逻辑与超协调表演算(英文)

源自当今互联网的语义网研究的目的是定义信息语义和网络服务,因此需要赋予网络智能以便能够自动对网络内容进行推理。各种描述逻辑(DLs)在语义网的研究中扮演着重要角色,构成了W3C推荐的网络本体语言(OWL)的基础,而OWL源于为达到语义网目标的人工智能(AI)本体论研究。语义网的知识和数据量巨大、分散、来源众多且因此通常不具有协调性。因此,必须开发针对非协调本体的实用的推理技术。该文基于Hunter的拟经典逻辑(QCL),构造了新型超协调拟经典描述逻辑(QCDLs),避免了逻辑爆炸问题,同时,针对基于非周期TBox的知识库推理问题,建立了QCDLs语义表演算,进而定义了一种可靠、完备且可判定的推理关系,从而构建了完整的语义网推理框架。与其他重要的超协调描述逻辑进行了比较,结果表明QCDLs具有更强的表达语义和推理能力,并且其相关行为在目标层次上表现出经典性。     

莱布尼兹的科学观—知识的数学化

本文论述了莱布尼兹的科学观在于知识的数学化以及为此所作的努力,即建立以普遍符号和推理演算为中心内容的通用语言代替自然语言,揭示了莱布尼兹发明微积分的思想根源,指出莱布尼兹科学观的哲学基础在于他关于事实真理和理性真理划分的理论。     

论高校教师分配制度的改革

为了高等学校的可持续发展 ,保证高校教育质量和办学水平的不断提高 ,改革和完善教师的收入、分配制度势在必行。本文试图以个案为例 ,探讨一个分类量化积分的分配模式 ,将教学、科研、管理等不同类型的工作统一在量化的岗位职责中     

LAN property for an ergodic Ornstein–Uhlenbeck process with Poisson jumps

In this article, we consider an ergodic Ornstein–Uhlenbeck process with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its jump intensity depend on unknown parameters. Considering the process discretely observed at high frequency, we derive the local asymptotic normality property. To obtain this result, Malliavin calculus and Girsanov’s theorem are applied to write the log-likelihood ratio in terms of sums of conditional expectations, for which a central limit theorem for triangular arrays can be applied.