Abstract: Convergence conditions of Taylor series to expected utility function are studied to guarantee the convergence of approximate solution to real solution.Under the setting of HARA utility,it is deducted that the convergence property of Taylor series is decided with how the rate of return deviates from the expansion point,then the approach is suggested of how to select expansion pointreasonably to guarantee the convergence of Taylor series to expected utility function.Based on the suggested approach,when return distribution is positively skewed,the general expansion point,i.e.the expectation of port folioreturn,is unreasonable.Finally the suggested approach is verified through numerical examples.

Key words: portfolio selection, Taylor series, expected utility, convergence