Knight不确定下持续业绩模型的最优消费—投资策略  

Optimal Consumption and Portfolio with Consistent Performance under Knight Uncertainty

作　　者：田德建 方洁 TIAN Dejian;FANG Jie(School of Mathematics,China University of Mining and Technology,Xuzhou,221116,China)

机构地区：[1]中国矿业大学数学学院,徐州221116

出　　处：《应用概率统计》2022年第3期402-412,共11页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:12171471)资助.

摘　　要：本文研究了Knight不确定下持续业绩模型的最优消费—投资策略问题.投资者对风险资产的预期收益率具有Knight不确定性,该不确定性由κ-无知模糊模型来刻画.持续业绩模型对财富过程采取了动态限制,要求财富水平不低于过去财富过程的加权平均.在无穷时间情形下,借助于HJB方程和验证定理得到了该模型下的最优消费–投资策略的显式解.The paper investigates the optimal consumption and portfolio with consistence performance under Knightian uncertainty.The agent has Knightian uncertainty for the expected return of risky asset,which is characterized by κ-ignorance model.Consistent performance model asks for a dynamic wealth constraint,which requires the wealth always stays at or above the weighted average of the entire historical wealth levels.In the infinite time horizon,we obtain the optimal consumption and portfolio explicit solution for the model by the HJB equation and verification theorem.

关 键 词：Knight不确定 持续业绩 财富约束 最优策略 

分 类 号：O211[理学—概率论与数理统计]