Abstract: Taking into account the limitations of risk measures such as variance, lower semi-variance and absolute deviation, and the fact that single-stage investment decision does not accord with investors' actual investment behavior, Value-at-Risk (VaR) is applied in this paper as a measure of risk for multi-stage portfolio optimization. Because short selling is not allowed in Chinese stock market, we consider both transaction costs and investment proportions in constraints and establish a multi-stage mean-VaR portfolio optimization model. Considering that PSO has the advantages of fast convergence, simple structure and less parameters to be regulated, the proposed multi-stage portfolio optimization model is solved by using PSO with penalty function processing mechanism. The optimal investment strategy at each stage under different paths is obtained. It can be seen from the results that the investor's investment behavior is consistent under different investment paths, buying the stocks they are optimistic about in the first stage. After the fluctuation of the stock market in the first stage, the investor continues to buy the stocks which are optimistic in the second stage. Meanwhile, the investor does not buy or sell stocks that are not good. This kind of investment behavior accords with the actual investment behavior of investors. Thus the proposed model is reasonable.

Key words: multi-stage, particle swarm optimization, Value-at-Risk, transaction costs