本文選題：無風(fēng)險(xiǎn)利率 + 等價(jià)鞅測度��； 參考：《西北師范大學(xué)》2013年碩士論文

【摘要】：金融數(shù)學(xué)的一個(gè)重要理論基礎(chǔ)是：在有限個(gè)資產(chǎn)和有限期的假設(shè)下,市場無套利等價(jià)于存在等價(jià)鞅測度,使得貼現(xiàn)的資產(chǎn)價(jià)格過程為鞅(資產(chǎn)定價(jià)第一定理).更進(jìn)一步說,如果市場是完全的,則無套利假設(shè)等價(jià)于存在唯一的等價(jià)鞅測度(資產(chǎn)定價(jià)第二定理).從這一結(jié)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(chǎn)的定價(jià)揭示了風(fēng)險(xiǎn)中性概率測度的內(nèi)在機(jī)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(fēng)險(xiǎn)中性定價(jià)本質(zhì)上是一個(gè)轉(zhuǎn)換過程即通過更正未來現(xiàn)金流的預(yù)期概率，將資產(chǎn)定價(jià)問題轉(zhuǎn)化為利用無風(fēng)險(xiǎn)利率進(jìn)行貼現(xiàn)的問題.然后使風(fēng)險(xiǎn)中性定價(jià)方法將任意定價(jià)問題放到一個(gè)統(tǒng)一的理論框架中：所有資產(chǎn)的定價(jià)都將按照無風(fēng)險(xiǎn)利率取得收益.最后給出了測度變換在完全市場中動(dòng)態(tài)最優(yōu)組合選擇中的應(yīng)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(fèi)問題，將市場系數(shù)由時(shí)間的確定性函數(shù)推廣到隨機(jī)函數(shù)情形,建立了數(shù)學(xué)模型；進(jìn)一步又根據(jù)現(xiàn)實(shí)當(dāng)中投資者對于不同方面的消費(fèi)會(huì)產(chǎn)生不同的滿足感和幸福感,又將消費(fèi)分成三部分得出了一些結(jié)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(xué)位授予單位】：西北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F830.9;F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

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2 韓琦;包守鴻;胡永云;;完全市場中的資產(chǎn)定價(jià)——有限離散時(shí)間情形[J];金融理論與實(shí)踐;2012年09期

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本文編號(hào)：1774279