等价鞅测度在资产定价中的应用

发布时间：2018-04-19 18:47

本文选题：无风险利率 + 等价鞅测度　；参考：《西北师范大学》2013年硕士论文

【摘要】：金融数学的一个重要理论基础是：在有限个资产和有限期的假设下,市场无套利等价于存在等价鞅测度,使得贴现的资产价格过程为鞅(资产定价第一定理).更进一步说,如果市场是完全的,则无套利假设等价于存在唯一的等价鞅测度(资产定价第二定理).从这一结果发展起来的一系列方法称为鞅方法.鞅方法使得金融理论中的许多问题得到相对简明的表示. 在完备市场的框架下本文的主要工作有：第一部分通过三种资产的定价揭示了风险中性概率测度的内在机理,并给出了合理的解释；第二部分首先通过讨论有限状态模型中的测度变换问题,来说明风险中性定价本质上是一个转换过程即通过更正未来现金流的预期概率，将资产定价问题转化为利用无风险利率进行贴现的问题.然后使风险中性定价方法将任意定价问题放到一个统一的理论框架中：所有资产的定价都将按照无风险利率取得收益.最后给出了测度变换在完全市场中动态最优组合选择中的应用；第三部分研究了在完全市场的条件下基于效用最大化的最优投资问题和最优投资-消费问题，将市场系数由时间的确定性函数推广到随机函数情形,建立了数学模型；进一步又根据现实当中投资者对于不同方面的消费会产生不同的满足感和幸福感,又将消费分成三部分得出了一些结论.
[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.
【学位授予单位】：西北师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224

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