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A variational inequality arising from European option pricing with transaction costs

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Science China Mathematics 2008年第5期51卷 935-954页

作者： YI FaHuai YANG Zhou School of Mathematical Sciences South China Normal UniversityCuangzhou 510631China

In this paper we present a method which can transform a variational inequality with gradient constraints into a usual two obstacles problem in one dimensional case.The prototype of the problem is a parabolic variational inequality with the constraints of two first order differential inequalities arising from a two-dimensional model of European call option pricing with transaction costs.We obtain the monotonicity and smoothness of two free boundaries.

关键词： option pricing transaction costs free boundary variational inequality

On nonlinear ill-posed inverse problems with applications to pricing of defaultable bonds and option pricing

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Science China Mathematics 2009年第6期52卷 1157-1168页

作者： POUZO Demian Department of Economics New York University New York NY 10012 USA

This paper considers the estimation of an unknown function h that can be characterized as a solution to a nonlinear operator equation mapping between two infinite dimensional Hilbert spaces. The nonlinear operator is unknown but can be consistently estimated, and its inverse is discontinuous, rendering the problem ill-posed. We establish the consistency for the class of estimators that are regularized using general lower semicompact penalty functions. We derive the optimal convergence rates of the estimators under the Hilbert scale norms. We apply our results to two important problems in economics and finance: (1) estimating the parameters of the pricing kernel of defaultable bonds; (2) recovering the volatility surface implied by option prices allowing for measurement error in the option prices and numerical error in the computation of the operator.

关键词： nonlinear ill-posed inverse problems Hilbert Scales optimal convergence rates pricing of defaultable bonds option prices

Put-call ratio predictability of the 50ETF option

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Economic and Political Studies 2019年第3期7卷 352-376页

作者： Jianhua Gang Yang Zhao Xinchen Ma School of Finance Renmin University of ChinaBeijingPR China International College Renmin University of ChinaBeijingPR China Hanqing Advanced Institute of Economics and Finance Renmin University of ChinaBeijingPR China

This article investigates the predictive power of the put-call ratios(PCRs)implied by China’s 50ETF option on the 50ETF return and its variance.By using simple partitional regressions,the relationship between the PCR and the 50ETF return is tested.This study conducts tests on their robustness based on different horizons,market conditions,moneyness status and time to maturity.Empirical results indicate that the PCR is a strong forward-looking indicator of the variance of 50ETF returns.A robust and negative correlation is detected.A significant linear correlation between the PCR and the 50ETF return only exists during the market crash.This study shows evidence that the PCR as seen in common trading practices may be misused and indicates a potential way of using it.

关键词： 50ETF option put-call ratio partitional OLS

基于优化子目标数的option-Critic算法

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计算机学报 2021年第9期44卷 1922-1933页

作者：刘成浩朱斐刘全苏州大学计算机科学与技术学院江苏苏州215006 苏州大学江苏省计算机信息处理技术重点实验室江苏苏州215006

时间抽象是分层强化学习中的重要研究方向,而子目标是时间抽象形成的核心元素.目前,大部分分层强化学习需要人工给出子目标或设定子目标数量.然而,在很多情况下,这不仅需要大量的人工干预,而且所作设定未必适合对应场景,在动态环境未知... 详细信息

时间抽象是分层强化学习中的重要研究方向,而子目标是时间抽象形成的核心元素.目前,大部分分层强化学习需要人工给出子目标或设定子目标数量.然而,在很多情况下,这不仅需要大量的人工干预,而且所作设定未必适合对应场景,在动态环境未知的指导下,这一问题尤为突出.针对此,提出基于优化子目标数的option-Critic算法(option-Critic algorithm based on Sub-goal Quantity Optimization,OC-SQO),增加了智能体对环境的探索部分,通过与环境的简单交互,得到适用于应用场景的初始子目标数量估值,并在此基础上识别子目标,然后利用通过策略梯度生成对应的抽象,使用初态、内部策略和终止函数构成的三元组表示,以此进行训练,根据交互得到的抽象改变当前状态,不断迭代优化.OC-SQO算法可以在任意状态下开始执行,不要求预先指定子目标和参数,在执行过程中使用策略梯度生成内部策略、抽象间策略和终止函数,不需要提供内部奖赏信号,也无需获取子目标的情况,尽可能地减少了人工干预.实验验证了算法的有效性.

关键词：分层深度强化学习时间抽象子目标强化学习 option

基于可中断option的在线分层强化学习方法

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通信学报 2016年第6期37卷 65-74页

作者：朱斐许志鹏刘全伏玉琛王辉苏州大学计算机科学与技术学院江苏苏州215006 吉林大学符号计算与知识工程教育部重点实验室吉林长春130012

针对大数据体量大的问题,在Macro-Q算法的基础上提出了一种在线更新的Macro-Q算法(MQIU),同时更新抽象动作的值函数和元动作的值函数,提高了数据样本的利用率。针对传统的马尔可夫过程模型和抽象动作均难于应对可变性,引入中断机制,提... 详细信息

针对大数据体量大的问题,在Macro-Q算法的基础上提出了一种在线更新的Macro-Q算法(MQIU),同时更新抽象动作的值函数和元动作的值函数,提高了数据样本的利用率。针对传统的马尔可夫过程模型和抽象动作均难于应对可变性,引入中断机制,提出了一种可中断抽象动作的Macro-Q无模型学习算法(IMQ),能在动态环境下学习并改进控制策略。仿真结果验证了MQIU算法能加快算法收敛速度,进而能解决更大规模的问题,同时也验证了IMQ算法能够加快任务的求解,并保持学习性能的稳定性。

关键词：大数据强化学习分层强化学习 option 在线学习

面向option的k-聚类Subgoal发现算法

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计算机研究与发展 2006年第5期43卷 851-855页

作者：王本年高阳陈兆乾谢俊元陈世福南京大学计算机软件新技术国家重点实验室铜陵学院计算机科学与技术系铜陵244000

在学习过程中自动发现有用的Subgoal并创建option,对提高强化学习的学习性能有着重要意义.提出了一种基于k-聚类的Subgoal自动发现算法,该算法能通过对在线获取的少量路径数据进行聚类的方法抽取出Subgoal.实验表明,该算法能有效地发现... 详细信息

在学习过程中自动发现有用的Subgoal并创建option,对提高强化学习的学习性能有着重要意义.提出了一种基于k-聚类的Subgoal自动发现算法,该算法能通过对在线获取的少量路径数据进行聚类的方法抽取出Subgoal.实验表明,该算法能有效地发现所有符合要求的Subgoal,与Q-学习和基于多样性密度的强化学习算法相比,用该算法发现Subgoal并创建option的强化学习算法能有效提高A-gent的学习速度.

关键词：分层强化学习 option 子目标

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基于探索密度的option子目标发现算法

模式识别与人工智能 2007年第2期20卷 236-240页

作者：孟江华朱纪洪孙增圻清华大学计算机科学与技术系智能技术与系统国家重点实验室北京100084

提出状态探索密度的概念,通过检测状态对智能体探索环境能力的影响来发现学习的子目标并构建对应的 option.用该算法创建 option 的再励学习算法能有效提高学习速度.算法具有和任务无关、不需要先验知识等优点,构造出的 option 在同一... 详细信息

提出状态探索密度的概念,通过检测状态对智能体探索环境能力的影响来发现学习的子目标并构建对应的 option.用该算法创建 option 的再励学习算法能有效提高学习速度.算法具有和任务无关、不需要先验知识等优点,构造出的 option 在同一环境下不同任务间可以直接共享.

关键词：递阶再励学习 option 探索密度(ED)

One-Year Outcomes of Women Started on Antiretroviral Therapy during Pregnancy before and after the Implementation of option B+ in Malawi: A Retrospective Chart Review from Three Facilities

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World Journal of AIDS 2014年第3期4卷 332-337页

作者： Alfred A. Kamuyango Lisa R. Hirschhorn Wenjia Wang Perry Jansen Risa M. Hoffman Department of Global Health and Social Medicine Harvard Medical School Boston USA Department of Medicine and Division of Infectious Diseases David Geffen School of Medicine University of California Los Angeles USA Department of Pathology College of Medicine University of Malawi Blantyre Malawi Department of Statistics University of California Los Angeles USA Hope Medical Centre Lilongwe Malawi

Objective: To compare one-year outcomes of women started on antiretroviral therapy (ART) during?pregnancy in the pre-option B+ era to those in the option B+ era. Methods: A retrospective chart review was performed at three sites in Malawi. Women were included in the “pre-option B+” cohort if they started ART during pregnancy for a CD4 count 3?or WHO 3/4 condition and in the “option B+” cohort if they started ART during pregnancy regardless of CD4 count or clinical stage. One-year outcomes were compared using Fisher’s exact and ANOVA F-tests. Results: A higher proportion of women in the pre-option B+ cohort started ART at WHO stage 3/4 (11.9% versus 1.1%, P option B+ cohort had poor adherence or defaulted, these differences were not significant. Conclusions: At our study sites, the transition to option B+ has been associated with ART initiation in women with less advanced HIV infection, improved medication tolerability, and lower mortality. Further research is needed to better understand outcomes of option B+.

关键词： Antiretroviral Therapy Pregnancy option B+ Prevention of Mother-to-Child Transmission

option Pricing with Markov Switching in Uncertainty Markets

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Open Journal of Applied Sciences 2015年第5期5卷 191-198页

作者： Guoshuai Wang Dianli Zhao College of Science University of Shanghai for Science and Technology Shanghai China

In this paper, we present a stock model with Markov switching in the uncertainty markets, where the parameters of drift and volatility change according to the states of a Markov process. To price the option, we firstly establish a risk-neutral probability based on the uncertain measure given by Liu. Then a closed form of the European option pricing formula is obtained by applying the Laplace transforms and the inverse Laplace transforms.

关键词： Uncertainty Theory Markov Process Laplace Transform Put-Call Parity option Pricing