發(fā)布時(shí)間：2018-07-03 10:06

  本文選題：鞅理論 + 期權(quán)定價(jià)　； 參考：《哈爾濱工業(yè)大學(xué)》2012年碩士論文

【摘要】：鞅論是概率論中的一個(gè)重要獨(dú)立分支，是概率論與隨機(jī)過(guò)程等方面的基礎(chǔ)。鞅理論具有很多的實(shí)際意義，在定價(jià)決策和控制模型中都起著重要的作用，我們可以通過(guò)鞅論框架的構(gòu)造使復(fù)雜問(wèn)題簡(jiǎn)單化，因此被廣泛使用，同時(shí)鞅論還滲透到統(tǒng)計(jì)分析、調(diào)和分析、Banach空間幾何學(xué)以及隨機(jī)分析等方面，同時(shí)取得了豐富的成果。 本文主要內(nèi)容分為兩部分，第一部分綜述了鞅的理論，，分經(jīng)典鞅論和現(xiàn)代鞅論兩部分來(lái)介紹，經(jīng)典鞅論內(nèi)容主要包括離散時(shí)間參數(shù)鞅和連續(xù)時(shí)間參數(shù)鞅的定義、性質(zhì)、不等式、收斂定理、停時(shí)定理等。現(xiàn)代鞅論內(nèi)容主要包括鞅的分解、可積變差鞅、平方可積鞅、局部鞅、半鞅、鞅的極限理論和鞅觀點(diǎn)下的隨機(jī)積分問(wèn)題。其中鞅理論和隨機(jī)積分知識(shí)相結(jié)合形成鞅方法，在金融領(lǐng)域有很重要的實(shí)際意義。 第二部分的內(nèi)容主要是關(guān)于鞅理論的應(yīng)用，我們分別引入了單期模型、多期模型和經(jīng)典的Black—Scholes期權(quán)定價(jià)模型，通過(guò)鞅理論的知識(shí)對(duì)這些模型進(jìn)行分析，得到相應(yīng)的結(jié)果，最后建立基于指數(shù)Ornstein-Uhlenbeck過(guò)程的帶有紅利支付的不確定執(zhí)行價(jià)格的期權(quán)模型，并分別計(jì)算出在歐式期權(quán)和美式期權(quán)的情況下期權(quán)不同的定價(jià)�？梢钥闯鲼崩碚搩�(nèi)容在金融領(lǐng)域期權(quán)定價(jià)方面具有很強(qiáng)的實(shí)用價(jià)值，隨著鞅理論的不斷完善給金融領(lǐng)域的相關(guān)衍生品定價(jià)提供了理論基礎(chǔ)。
[Abstract]:Martingale theory is an important independent branch of probability theory and the basis of probability theory and stochastic process. Martingale theory has a lot of practical significance and plays an important role in pricing decision and control model. We can simplify complex problems by constructing martingale theory frame, so it is widely used, and martingale theory also permeates statistical analysis. Harmonic analysis of Banach space geometry and random analysis, and achieved a wealth of results. The main contents of this paper are divided into two parts. The first part summarizes the theory of martingale, which is introduced in two parts: classical martingale theory and modern martingale theory. The classical martingale theory mainly includes the definition, properties, inequalities of discrete time parameter martingale and continuous time parameter martingale. Convergence theorem, stop time theorem and so on. The content of modern martingale theory mainly includes the decomposition of martingale, integrable martingale, square integrable martingale, local martingale, semimartingale, martingale limit theory and stochastic integral problem under martingale viewpoint. Martingale theory and stochastic integral knowledge combine to form martingale method, which is of great practical significance in the field of finance. The second part is mainly about the application of martingale theory. We introduce the single-period model, multi-period model and the classic Black-Scholes option pricing model respectively. Through the knowledge of martingale theory, we analyze these models and get the corresponding results. Finally, an option model with uncertain executive price with dividend payment is established based on the exponential Ornstein-Uhlenbeck process, and the different pricing of options is calculated in the case of European option and American option respectively. It can be seen that martingale theory has a strong practical value in the field of financial option pricing. With the continuous improvement of martingale theory, it provides a theoretical basis for the pricing of related derivatives in the financial field.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：O211.6;F830.9

【參考文獻(xiàn)】

相關(guān)期刊論文 前6條

1 閆海峰,劉三陽(yáng),李文強(qiáng);股票價(jià)格遵循指數(shù)O-U過(guò)程的最大值期權(quán)定價(jià)[J];工程數(shù)學(xué)學(xué)報(bào);2004年03期

2 肖振紅;王U

本文編號(hào)：2093280