基于随机控制理论的最优投资与效用无差别定价研究

发布时间：2018-03-01 18:42

本文关键词： 不完备市场最优投资效用无差别定价 HJB方程　出处：《西南财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：投资组合选择和金融资产定价问题一直是现代金融理论研究的核心内容。关于动态投资组合的研究主要是在Merton模型的基础上进行改进,探讨不同投资环境下风险厌恶投资者的最优选择。关于完备市场金融资产定价的研究主要是基于无套利理论,但是当市场不完备时,由于存在多个等价鞅测度而无法得到资产的唯一价格。HodgesNeuberger提出的效用无差别定价理论为解决不完备市场中金融资产定价问题提供了理论基础。因此,本文基于随机控制理论研究以下两个问题： (1)具有线性消费模式的最优投资。当投资者具有线性消费时,就有可能发生破产,而传统的Merton问题并没有考虑破产的可能性。本文利用随机控制理论得到了投资者的最优投资策略以及价值函数满足的偏微分方程,然后分别在指数效用和幂效用函数下得到了投资者的最优投资策略的显示解。 (2)不完备市场中风险资产的效用无差别定价。在不完备市场中,首先假设利率是常数时,根据效用无差别定价理论得到了风险资产的效用无差别价格满足的偏微分方程,并且在指数效用函数下得到了效用无差别价格的显示解。其次假设市场具有Ho-Lee利率模型,重新得到了不完备市场中风险资产的效用无差别价格满足的偏微分方程。
[Abstract]:Portfolio selection and financial asset pricing have always been the core contents of modern financial theory. The research on dynamic portfolio is mainly based on Merton model. This paper discusses the optimal choice of risk-averse investors in different investment environments. The research on the pricing of financial assets in the complete market is mainly based on the theory of no arbitrage, but when the market is not complete, Due to the existence of multiple equivalent martingale measures, it is impossible to obtain the unique price of assets. HodgesNeuberger's Utility Non-differential pricing Theory provides a theoretical basis for solving the pricing problem of financial assets in incomplete markets. In this paper, based on stochastic control theory, the following two problems are studied:. An optimal investment with a linear consumption pattern. When an investor has a linear consumption, it is possible to go bankrupt. However, the traditional Merton problem does not consider the possibility of bankruptcy. In this paper, the optimal investment strategy of investors and the partial differential equation satisfying the value function are obtained by using stochastic control theory. Then under the exponential utility function and the power utility function, the display solution of investors' optimal investment strategy is obtained. In incomplete market, when the interest rate is constant, the partial differential equation of utility nondifferential price is obtained according to the theory of utility nondifferential pricing. Moreover, under the exponential utility function, we obtain the explicit solution of the utility undifferentiated price. Secondly, assuming that the market has the Ho-Lee interest rate model, we obtain the partial differential equation of the utility of the risk asset in the incomplete market.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

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