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In this paper, we study the global optimality of polynomial portfoliooptimization (PPO). The PPO is a kind of portfolio selection model withhigh-order moments and flexible risk preference parameters. We introduce aperturbation sample average approximation method, which can give a robustapproximation of the PPO in form of linear conic optimization. The approximatedproblem can be solved globally with Moment-SOS relaxations. We summarize asemidefinite algorithm, which can be used to find reliable approximations ofthe optimal value and optimizer set of the PPO. Numerical examples are given toshow the efficiency of the algorithm.

Global optimization for the portfolio selection model with high-order moments