Optimal consumption and portfolio selection with Epstein–Zin utility under general constraints  

作　　者：Zixin Feng Dejian Tian 

机构地区：[1]School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China [2]School of Mathematics and Statistics,Wuhan University,Wuhan 430070,China

出　　处：《Probability, Uncertainty and Quantitative Risk》2023年第2期281-308,共28页概率、不确定性与定量风险（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12171471).

摘　　要：The paper investigates the consumption–investment problem for an investor with Epstein–Zin utility in an incomplete market.Closed but not necessarily convex constraints are imposed on strategies.The optimal consumption and investment strategies are characterized via a quadratic backward stochastic differential equation(BSDE).Due to the stochastic market environment,solutions to this BSDE are unbounded,so the BMO argument breaks down.After establishing the martingale optimality criterion and carefully selecting Lyapunov functions,the verification theorem is ultimately obtained.In addition,several examples and numerical simulations of optimal strategies are provided and illustrated.

关 键 词：Closed constraints Consumption–investment problem Epstein–Zin utility Quadratic BSDE 

分 类 号：O21[理学—概率论与数理统计]