In this paper,we study the global optimality of polynomial portfolio optimization(PPO).The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters.We introduce a pert...In this paper,we study the global optimality of polynomial portfolio optimization(PPO).The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters.We introduce a perturbation sample average approximation method,which can give a robust approximation of the PPO in form of linear conic optimization.The approximated problem can be solved globally with Moment-SOS relaxations.We summarize a semidefinite algorithm,which can be used to find reliable approximations of the optimal value and optimizer set of the PPO.Numerical examples are given to show the efficiency of the algorithm.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12071399 and 12171145)Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(No.2018WK4006)Project of Hunan National Center for Applied Mathematics(No.2020ZYT003).
文摘In this paper,we study the global optimality of polynomial portfolio optimization(PPO).The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters.We introduce a perturbation sample average approximation method,which can give a robust approximation of the PPO in form of linear conic optimization.The approximated problem can be solved globally with Moment-SOS relaxations.We summarize a semidefinite algorithm,which can be used to find reliable approximations of the optimal value and optimizer set of the PPO.Numerical examples are given to show the efficiency of the algorithm.
