摘要
本文采用Merton提出的处理捐赠型基金的连续时间模型的一般框架,分析了在风险资产为几何布朗运动,效用函数为CRRA效用函数,且捐赠型基金有动态最低支出时的最优支出策略和最优投资策略,结果表明存在一条策略基准线,当基金的总资产在策略基准线之上时,基金管理人关于基金支出与投资策略的选择与不存在最低支出的要求时所作出的决策是一样的.但是一旦基金的总资产低于这条策略基准线时,基金管理人便需要考虑到基金将来必要的支出,并实际影响到他对投资策略的选择,此时基金管理人可作的最优选择是:最低的支出和一种为复制幂收益函数期权的CPPI投资策略.
In this paper we obtain the optimal consumption and optimal investment strategies of the donation funds with dynamic minimal consumption levels by adopting the contimuous time frameworks of donation fund problems proposed by Merton and assuming that the risky asset is geometric brownian motion and utility function is CRRA function.Our results show that there exists a strategy benchmark line, when the total wealth is above the benchmark line the fund managers can choose their strategies as if there is no minimal consumption level, when the total wealth is below the benchmark line the fund managers have to think more about the future consumption and in fact this minimal consumption constraints have impact on the optimal strategies, the optimal choices of the fund managers in this case are that they consume the minimal levels and invest according to CPPI strategy which is the hedging strategy of the option with power payoff function.
出处
《应用数学学报》
CSCD
北大核心
2005年第3期396-404,共9页
Acta Mathematicae Applicatae Sinica
基金
中国科学院"百人工程"
国家杰出青年基金资助项目
