随机波动下的确定缴费型养老金投资问题

发布时间：2018-03-27 17:44

本文选题：确定缴费计划养老金　切入点：CEV随机波动模型　出处：《天津大学》2014年硕士论文

【摘要】：随着全球人口老龄化现象日益加剧，养老金的保值、增值问题备受关注。通过投资来实现养老金的保值增值是一种常用的手段。但投资伴随着风险，因此需要寻找最优的投资策略。在实际的风险资产市场中，由于存在许多不确定的事件，像泡沫、灾难、金融危机等，都会对风险资产的收益和方差产生很大的影响。有大量的实证研究表明风险资产（如股票）的收益和方差都是随机的。所以，在风险资产的收益率和方差都是随机的条件下，对养老金计划的最优投资策略进行研究，无论是在理论上，还是在养老金实务中，都具有非常重要的意义。本文对确定缴费计划养老金，在养老金基金投资于无风险资产和风险资产的条件下，研究使得期望财富最大的最优投资策略。在指数效用函数和幂效用函数下，，分别得到使得期望财富最大的最优投资策略，以及最大期望财富效用函数的显示解。本文就风险资产服从于CEV模型、Heston模型与Stein-Stein模型的不同情况分别进行讨论，第三、四、五章分别研究了在以上三种随机波动率方程下的确定缴费型养老金计划的最优投资问题。通过求解目标函数所对应的HJB方程得到最优投资策略和最优值函数的明确表达式。
[Abstract]:Along with the global aging population is increasing, the pension value, value-added concern. Through investment to achieve increasing the value of the pension is a commonly used means. But with the investment risk, therefore it is necessary to find the optimal investment strategy. In the actual risk in the asset market, because there are many uncertain events, like bubble, disaster, such as the financial crisis, will have a great effect on the risk of asset return and variance. There are a large number of empirical studies show that the risk of assets (such as stocks) the return and variance are random. So, in the return of risk assets and the variance are random conditions of optimal investment the strategy of pension plans, either in theory or in practice, pension, has a very important significance.
Based on the defined contribution pension plan, pension fund to invest in the riskless asset and risky asset under the condition of the optimal investment strategy for the largest expected wealth. In the exponential utility function and power utility function, the optimal investment strategy to get the expected wealth maximum respectively, and the maximum expected utility of wealth function display solutions.
In this paper, the risk of assets subject to different conditions on the CEV model, Heston model and Stein-Stein model are discussed, respectively, third, fourth, five chapter studies three kinds of stochastic volatility equation under the optimal investment problem contribution pension scheme was determined in the above. By solving the HJB equation corresponding to the target function to get a clear expression of the optimal investment strategy and the optimal value function.

【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F842.67;F224

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