Mathematical finance

Problem of Option Pricing in Mathematical Finance

数学金融学中的期权定价问题

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In the fifties of last century, Markowitz found portfolio selection theory. This theory applied mathematical tools to finance problems firstly.

上世纪五十年代，Markowitz提出了投资组合选择理论，这一理论首次将数理工具引入到金融问题中。

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His book is a critique bordering on an assault on mathematical or quantitative finance.

本书是对数学（或者定量）金融学几近抨击的一种批判。

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In recent years, with the vigorous development of the financial market, the theory for the option pricing has became the research focus of the mathematical finance.

几年来，随着金融市场的蓬勃发展，期权定价理论成为数理金融的一个研究重点。

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During the development of financial economics and mathematical finance, the instability always existed in the whole system. Therefore, the main ingredient in order to avoid risk capital theory and financial instruments has got a wide range of study and attention.

在人类社会经济金融系统的发展过程中，系统的不稳定性贯穿始终，由此以波动为主要成分的用以规避风险的投资理论和相应的金融工具一直是理论界和实务界所关注的重要课题。

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The emergence of portfolio theory really makes mathematical methods enter the investment field. Thus, mathematical finance as an independent branch of the finance theory develops quickly.

投资组合理论的产生使得数理化方法真正进入到投资领域，使得数理金融学作为金融学的一个独立的分支迅速发展起来。

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Financial Engineering, Financial Mathematics, Mathematical Finance, Computa.

然而无论是叫金融工程。

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This paper introduces the problem of option pricing in mathematical finance.

粗略地介绍数学金融学中的期权定价问题.

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From then on, the research of modern Mathematical Finance gained rapid development with tremendous achievements. Most remarkable of all, the Black-Scholes model has not been obtained plentiful results in theoretical research, but also been applied in financial market broadly.

从此，金融数学的研究得到了蓬勃的发展，取得了非常丰硕的成果，而且应用于金融市场，受到广泛的欢迎。

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From historical viewpoint, it can be found that modern financial theories develop in quantitative trend and mathematical finance has been faced with challenges since its birth.

历史地考察现代金融理论的演进，可发现其不断呈现数量化的发展趋势，数理金融也经历了产生、发展到面临挑战的历程；

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The networks algorithm on mathematical finance model

数理金融模型的神经网络算法

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Fractional Black-Scholes Model of Mathematical Finance and Applications

数学金融的分数次Black-Scholes模型及应用

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In mathematical finance, there has been a large number of literature on the estimation of the continuous-time models, however, there is relatively little effort on specification analysis for continuous-times models.

在金融数学中，已经有大量的文献研究连续时间模型估计问题，但有关连续时间模型设定方面的工作却相对较少。

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In this dissertation, on the basis of the stochastic integral theory of the fractional Brownian Motion, we studied fractional Black-Scholes Model of mathematical finance with arbitrary Hurst parameter are studied systematically and comprehensively.

本文在分数次布朗运动的积分理论的基础上，对数学金融的具有任意Hurst参数的分数次Black-Scholes模型进行了全面系统的研究。

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This paper proposes the neural networks method of solving the model of mathematical finance by means of the neural networks ideas, and theoretically and empirically proves the existence, stability and efficiency of the results.

借助于神经网络的思想，提出了求解数理金融模型的神经网络算法，从理论和应用两个方面证明了解的存在性、稳定性和有效性。

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From then on, BSDE is further studied and applied widely in stochastic control, partial differential equation ( PDE), mathematical finance and economics.

倒向随机微分方程在随机控制、偏微分方程、数理金融、经济等领域都有着广泛的应用。

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Merton made a major breakthrough in the pricing of financial derivatives, rapid progress has been gained in the theory and application of mathematical finance.

Merton等三人在确定金融衍生产品价值的创造性贡献以来，数学金融学的理论与应用研究得到了快速发展，取得了丰硕成果。

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From the opening chapter, "playing God", Triana maintains that the fundamental assumptions on which mathematical finance theory are based are wrong.

在开篇章节“扮演上帝”（playing god）中，特里亚纳坚称，数学金融学理论所基于的根本假设是错误的。

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For it seems likely that, no matter how hard observers such as Triana and Taleb try to demolish it, mathematical finance is not going away.

因为似乎无论特里亚纳和塔勒布这样观察家多么努力地试图推翻数学金融学，它很可能都不会消失。

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Mathematical Finance is intersect of Mathematic and Finance, and introduces principal modern Mathematical methods of Mathematical Finance, and give a discription of principal theory and methods of Mathematical Finance: stochastic differential equation and stochastic optimal control.

金融数学是数学与金融学的交叉，又介绍了金融数学主要用到的现代数学方法，并详细阐述了本文用到的主要定理和方法：随机微分方程和随机最优控制。

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The basic ideas of behavioral finance is on the opposite of that of mathematical finance: traditional mathematical finance held the viewpoint that investors were rational and market was effective; however, behavioral finance takes the idea that investors are irrational and market is ineffective.

传统的数理金融学认为投资者是理性的，市场是有效的。而行为金融学认为投资者并不是完全理性的，市场并非是有效的。

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This is a breakthrough of modern Mathematical Finance.

这是现代金融数学的一项具有里程碑意义的突破性成果。

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Studying and Developing of the Mathematical Finance

数理金融的研究及其发展

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The first fundamental theorem of asset pricing is the one of two most fundamental theorems in mathematical finance. It mainly describes the fairness of a market which is one of the two most important properties of the market.

资产定价第一基本定理是数理金融学中的两大基本定理之一，它主要是描述市场的两大性质之一：市场公平性。

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The Financial Crisis of Southeast Asia and Mathematical Finance

金融危机与金融数学

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Research and teaching: Stochastic Process, Stochastic analysis, Risk theory, Financial Economics and Mathematical Finance.

主要研究和教学领域: 随机过程, 随机分析, 风险理论, 金融经济学,金融数学.

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Mathematical finance is a new frontier science, it is the intersection of mathematics and finance.

金融数学是一门新兴的边缘科学，是数学与金融学的交叉。

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At the same time, the researches on security investment deepened and associated with mathematical finance researches.

与此同时，证券投资研究日益深化，并逐步与数理金融研究融合。

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The theory of BSDEs and its applications-have been improved significantly, e.g* in mathematical finance and stochastic-control problems.

之后，倒向方程理论及相关应用开始了飞速发展，尤其是在金融数学和随机控制领域。

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The pricing of option is the core of mathematical finance.

期权定价理论是金融数学的核心内容。

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