分形市场假设下的未定权益定价应用数学专业论文.docxVIP

山东科技大学硕士学位论文摘要 山东科技大学硕士学位论文 摘要 PAGE PAGE 1 摘 要 未定权益的定价理论一直是金融数学研究的核心内容，本文考虑了分形市场假设下 的未定权益定价理论。 本硕士论文由三部分内容组成。 第一章主要介绍了所研究课题的背景。 第二章讨论了分形市场假设下有红利支付的未定权益定价。首先介绍了关于分数布 朗运动的定义，性质。在此基础上，我们分别讨论了有红利支付的欧式未定权益定价， 到期前任意时刻的欧式期权定价，两种奇异欧式期权定价公式，不同金融市场条件下的 未定权益定价模型。 第三章讨论了电力投资项目的实物期权特性，并用实物期权方法评价电力投资项目 的最优投资规则。首先我们建立了投资项目在单期投资假设下的最优投资规则，然后根 据电力项目投资过程的长期特性，在多期投资假设下对项目的最优投资规则做了评价。 并且将传统的投资规则和实物期权投资规则的进行了比较。 关键词：分数布朗运动 ；未定权益；奇异期权；实物期权 山东科技大学硕士学位论文Ab 山东科技大学硕士学位论文 Abstract ABSTRACT The pricing theory of the contingent claims has been the core contents of financial mathematic. This Masters thesis considered the contingent claims pricing theories under fractal market assumption. This Masters thesis is divided into three parts. In chapter one, we mainly introduce the background of the research topic. In chapter two, we discuss the contingent claims pricing under the fractal market assumption. Firstly, we introduce the definition, properties and integral theory of fractional Brownian motion. In section 2， we obtain the European contingent claims pricing formula from the price of underlying asset dividends payments. In section 3, we obtain the pricing formulas of European option at arbitrary time before maturity when the stock pays the bonus. In section 4,we obtain pricing formulas of two kinds of singular options. In section 5, we discuss the pricing model of contingent claims under different financial market assumption. In chapter three, we analyze real option characteristic and the optimal investment regulations of the electric power investment item. Firstly we introduce the optimize investment regulations under the single time. Then according to the characteristic of large investment item we analyze the optimal investment rule and make comparison between the NPV regular and real option regular. Keywords: fractional Brownian motion; contingent claims; singular option; real option 山东科技大学硕士学位论文目录 山东科技大学硕士学位论文 目录 目 录 1 绪论………………………………………