本文選題：無風險利率 + 等價鞅測度　； 參考：《西北師范大學》2013年碩士論文

【摘要】：金融數(shù)學的一個重要理論基礎是：在有限個資產和有限期的假設下,市場無套利等價于存在等價鞅測度,使得貼現(xiàn)的資產價格過程為鞅(資產定價第一定理).更進一步說,如果市場是完全的,則無套利假設等價于存在唯一的等價鞅測度(資產定價第二定理).從這一結果發(fā)展起來的一系列方法稱為鞅方法.鞅方法使得金融理論中的許多問題得到相對簡明的表示. 在完備市場的框架下本文的主要工作有： 第一部分通過三種資產的定價揭示了風險中性概率測度的內在機理,并給出了合理的解釋； 第二部分首先通過討論有限狀態(tài)模型中的測度變換問題,來說明風險中性定價本質上是一個轉換過程即通過更正未來現(xiàn)金流的預期概率，將資產定價問題轉化為利用無風險利率進行貼現(xiàn)的問題.然后使風險中性定價方法將任意定價問題放到一個統(tǒng)一的理論框架中：所有資產的定價都將按照無風險利率取得收益.最后給出了測度變換在完全市場中動態(tài)最優(yōu)組合選擇中的應用； 第三部分研究了在完全市場的條件下基于效用最大化的最優(yōu)投資問題和最優(yōu)投資-消費問題，將市場系數(shù)由時間的確定性函數(shù)推廣到隨機函數(shù)情形,建立了數(shù)學模型；進一步又根據(jù)現(xiàn)實當中投資者對于不同方面的消費會產生不同的滿足感和幸福感,又將消費分成三部分得出了一些結論.
[Abstract]:An important theoretical basis of financial mathematics is that under the assumption of finite assets and a limited period of time, market arbitrage is equivalent to the existence of equivalent martingale measures, so that the discounted asset price process is martingale (asset pricing first principle). Furthermore, if the market is complete, the assumption of no arbitrage is equivalent to the existence of a unique equivalent martingale measure (the second theorem of asset pricing). A series of methods developed from this result are called martingale methods. Martingale method makes many problems in financial theory relatively concise. Under the framework of complete market, the main work of this paper is as follows: The first part reveals the intrinsic mechanism of risk-neutral probability measure through the pricing of three kinds of assets, and gives a reasonable explanation. In the second part, by discussing the measure transformation problem in the finite state model, it is shown that risk neutral pricing is essentially a conversion process, that is, by correcting the expected probability of future cash flow. The problem of asset pricing is transformed into the problem of discounting with risk free interest rate. Then the risk-neutral pricing method puts the arbitrary pricing problem into a unified theoretical framework: all assets will be priced at the risk-free rate of return. Finally, the application of measure transformation in dynamic optimal combination selection in complete market is given. In the third part, the optimal investment problem based on utility maximization and the optimal investment-consumption problem are studied under the condition of complete market. The market coefficient is extended from the deterministic function of time to the case of stochastic function, and the mathematical model is established. Further, according to the reality, investors will produce different satisfaction and happiness for different aspects of consumption, and then divide consumption into three parts to draw some conclusions.
【學位授予單位】：西北師范大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F830.9;F224

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本文編號：1774279