Abstract: Asset allocation means dividing investors' investments among different assets both in space and time.Although modern portfolio theory has developed to a highly sophisticated level and provided us with valuable theatrical models and application frameworks in steering assets in space,little is known about asset allocation in time.The core question of asset allocation in time is how to optimally select buying and selling time for different assets at different time,that is,optimal trading strategy design.Based on dynamis programming principles,this paper proposes an efficient algorithm for return-optimal trading strategy both for the case of trading with and without the constraint of maximum trading times,and implements the algorithm by using the data from Hong Kong stock market.The computation algorithm proposed in this paper is a linear time algorithm with respect to the number of trading periods and number of assets,and can be used in large-scale problem efficiently.

Key words: trading strategy, transaction cost, rate of return, dynamic programming, optimal solution