  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.
