Ornstein-Uhlenbeck模型下DC养老金计划的最优投资策略

发布时间：2018-05-11 17:03

本文选题：DC型养老基金计划 + 最优投资策略　；参考：《应用数学学报》2013年04期

【摘要】：本文研究了Ornstein-Uhlenbeck模型下确定缴费型养老金计划(简称DC计划)的最优投资策略,其中以最大化DC计划参与者终端财富(退休时其账户金额)的CRRA效用为目标.假定投资者可投资于无风险资产和一种风险资产,风险资产的瞬时收益率由Ornstein-Uhlenbeck过程驱动,该过程能反映市场所处的状态.利用随机控制理论,给出了相应的HJB方程与验证定理;并通过求解相应的HJB方程,得到了最优投资策略和最优值函数的解析式.最后分析了瞬时收益率对最优投资策略的影响,发现当市场向良性状态发展时,投资在风险资产上的财富比例呈上升趋势;当初始财富足够大且市场状态不变时,投资在风险资产上的财富比例几乎不受时间的影响.
[Abstract]:In this paper, the optimal investment strategy for determining contributory pension plan (DC plan) under Ornstein-Uhlenbeck model is studied. The goal is to maximize the CRRA utility of the terminal wealth of DC plan participants (the amount of their account at retirement). Assuming investors can invest in risk-free assets and a risky asset, the instantaneous return on risky assets is driven by the Ornstein-Uhlenbeck process, which reflects the market's state. By using stochastic control theory, the corresponding HJB equation and verification theorem are given, and the analytical expressions of optimal investment strategy and optimal value function are obtained by solving the corresponding HJB equation. Finally, the influence of instantaneous rate of return on the optimal investment strategy is analyzed. It is found that the proportion of wealth invested in risky assets increases when the market develops to a benign state, and when the initial wealth is large enough and the market state remains unchanged, The proportion of wealth invested in risky assets is almost unaffected by time.
【作者单位】：中山大学数学与计算科学学院;广东工业大学应用数学学院;中山大学管理学院中山大学金融工程与风险管理研究中心;中山大学岭南(大学)学院、中山大学金融工程与风险管理研究中心;
【基金】：国家自然科学基金重点项目(No71231008) 教育部人文社会科学研究青年基金项目(12YJCZH267) 广东省哲学社会科学规划(NoGD11YYJ07)资助项目
【分类号】：F224;F840

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