摩擦市场渐近无套利分析及应用研究

摘要本文研究了摩擦市场无套利的特征问题。首先，总结了(B,S)市场是无套利的充要条件：1）存在等价概率测度；2）存在最优消费策略；3）存在正的状态价格向量。

其次，基于以上三个关于摩擦市场的无套利等价性结论，结合现有金融学中衍生证券定价的研究成果，本文得出如下的结论：产品的可定价性意味着此类市场是无套利的。

最后，基于经典的Black-Scholes模型以及Harnack不等式等相关模型证实了这一结论。67262

作为对套利理论的进一步完善，本文简要分析了渐近套利问题。

毕业论文关键词无套利，等价概率测度，最优消费，状态价格， B-S模型， Harnack不等式，渐近套利

毕业设计说明书（论文）外文摘要

Title The Analysis And Application Of Asymptotic Arbitrage

Abstract

This paper studies the characteristics problem of no-arbitrage in friction market.

Firstly,the article summed up the necessary and sufficient conditions of no-arbitrage in (B,S) market :1）the existence of equivalent probability measure;2）the existence of optimal consumption policy; 3）the existence of positive state price vector.

Secondly,based on the above equivalent conclusions about no-arbitrage in friction market and combined with the research on derivative securities pricing in the existing finance,this article drew a new conclusion: product pricing implies that such markets can exist no arbitrage opportunities.

Finally, we validated the conlusion based on related models such as the classic Black-Scholes model and Harnack inequality.

As a further improvement of arbitrage theory , this paper analyzed briefly the problem of asymptotic arbitrage.

Keywords no arbitrage, equivalent probability measure, optimal consumption, state prices, B-S model, Harnack inequality, asymptotic arbitrage

1 绪论 1

1.1 引入 1

1.2 无套利的发展历史 1

1.3 未来套利研究的展望 2

1.4 经典的二项式模型简述 2

1.5 文章结构 4

1.6 本文的创新点 5

2 预备知识 6

2.1 几何Brown运动 7

2.2 Ito公式及其简单应用 7

2.3 Kolmogorov方程 8

3 无套利特性分析 8

3.1 无套利的等价条件 9

3.1.1 (B,S)市场上的无套利分析 9

3.1.2 存在最优消费时的无套利分析 10

3.1.3 状态价格与无套利分析 11

3.2 无套利问题的拓展 12

3.2.1 问题的提出 12

3.2.2 经典的B-S模型 13

3.2.3 无套利与B-S模型的关系 16

3.3 Harnack不等式与无套利 17

3.3.1 基本假设摩擦市场渐近无套利分析及应用研究:http://www.751com.cn/shuxue/lunwen_75392.html