模型不确定下最优消费和投资组合决策问题研究

发布时间：2018-04-03 23:56

本文选题：最优投资组合　切入点：模型不确定　出处：《安徽工程大学》2013年硕士论文

【摘要】：随着金融市场的不断发展,最优消费和投资组合决策问题为众多学者所关注.一些国内外学者已经对最优消费和投资模型从不同的角度作了研究,但大多都是在金融市场模型完全信任的假设下建立最优投资策略的,假设投资者对资产回报模型有完全的信心及不担心模型的不确定性.但随着金融市场的不断创新和发展,投资者往往担心模型的误定,试图寻找更加符合实际的投资模型.因此,本文基于现有的理论成果,结合当前经济的发展状况,分析了模型不确定性对最优消费和投资组合决策的影响.在考虑投资模型存在模型误定(即不确定性)的情况下,结合通胀环境和红利支付情形,运用随机最优控制的方法,建立最优消费和投资组合模型,使该模型具有更广泛的代表性和更切实际的经济意义. 首先,在模型不确定下考虑股票支付红利的情形.研究了带有递归偏好的投资者在考虑股票红利支付情形下的最优消费和投资组合.假设投资者担心模型的误定,因此寻求稳健的决策规则.我们考虑一个股票预期收益率遵循一个均值回复过程的金融市场.那么当投资者跨期替代弹性等于1和风险厌恶适中时,推导了最优消费和投资决策的显示解.给定股票收益率和预期收益率为负的相关系数时,通过数值模拟,发现模型不确定性厌恶增加了财富投资于股票的比例.同时股票支付红利也进一步加大了财富投资于股票的比例. 然后,在模型不确定下考虑通胀环境情形.探讨了不同通胀环境下的通胀波动率对最优消费和投资组合模型所产生的影响.建立投资者决策的值函数对应的HJB方程,根据特定的效用函数,推导了最优消费和投资决策的显示解.通过对数值模拟结果的分析可知,对模型不确定的担忧导致了短视需求的大幅减少,从而引起最优股权分配比率的下滑.但在考虑低通胀波动率的影响下,相对于无通胀情形,通胀对冲需求增加了最优股权分配比率；而在考虑高通胀波动率的影响时,相对于无通胀情形,通胀对冲需求则加剧了最优股权分配比率的下滑.
[Abstract]:With the development of financial market, the problem of optimal consumption and portfolio decision is concerned by many scholars.Some scholars at home and abroad have studied the optimal consumption and investment model from different angles, but most of them are based on the assumption that the financial market model is completely trusted to establish the optimal investment strategy.Assume that investors have complete confidence in the asset return model and do not worry about the uncertainty of the model.But with the continuous innovation and development of the financial market, investors often worry about the misdefinition of the model and try to find a more realistic investment model.Therefore, based on the existing theoretical results and combined with the current economic development, this paper analyzes the impact of model uncertainty on optimal consumption and portfolio decision.Considering the uncertainty of the investment model, the optimal consumption and investment portfolio model is established by using the stochastic optimal control method combined with the inflation environment and dividend payment.The model has more extensive representation and practical economic significance.Firstly, under the uncertainty of the model, the dividend payment is considered.The optimal consumption and portfolio of investors with recursive preference under the consideration of dividend payment are studied.Suppose that investors are worried about the misdefinition of the model, so they seek robust decision-making rules.We consider a financial market where the expected return on a stock follows an average recovery process.Then when the intertemporal substitution elasticity is equal to 1 and the risk aversion is moderate, the explicit solution of optimal consumption and investment decision is derived.Given the negative correlation coefficient between stock return and expected return, it is found by numerical simulation that uncertainty aversion increases the proportion of wealth invested in stocks.At the same time, dividends paid by stocks also further increased the proportion of wealth invested in stocks.Then, the inflation environment is considered under the uncertainty of the model.The influence of inflation volatility on the optimal consumption and investment portfolio model is discussed.The HJB equation corresponding to the value function of investor decision is established. According to the specific utility function, the display solution of optimal consumption and investment decision is derived.Through the analysis of the numerical simulation results, we can see that the worry about the uncertainty of the model leads to the sharp reduction of short-sighted demand, which leads to the decline of the optimal share allocation ratio.However, considering the impact of low inflation volatility, the demand for inflation hedging increases the optimal equity allocation ratio relative to the non-inflation situation, and when the impact of high inflation volatility is considered, it is relative to the non-inflation situation.Demand for inflation hedges has exacerbated the decline in the optimal equity allocation ratio.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.59;F224

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