Abstract: With the increasing interactivity of financial markets, the single risk market cannot meet the actual investment needs. There have been academic studies indicating that the fluctuation of asset returns in the market can be influenced by the economic cycle which shows different characteristics under different market conditions. Meanwhile, in the actual investment, investors often deviate from the expected utility theory. In this paper, under the framework of prospect theory and behavioral finance, an asset allocation problem among cross-markets with regime switching is studied. Hidden Markov regime switching-mixture normal distribution is constructed to describe time-varying regimes in the stock market, the bond market and the commodity market, the parameters of which are estimated by the Baum-Welch algorithm. Moreover, with scenarios generated under regime switching, a multi-period stochastic optimized model is constructed. Further, against the background of the stock market, the bond market and the commodity market in China, the performance of multi-period stochastic model is empirically analyzed by the use of rolling window method, which is compared with the results of standard dynamic model ignoring regime switching, equally weighted portfolio and hs300 index. It is concluded that compared with other portfolio, regime switching portfolio helps avoid risk, and under the prospect theory, regime switching information of hybrid markets can have an effect on optimal decision of prospect theory investors. The conclusions show that compared with risk investment with single market, the multi-period asset allocation of cross-markets under the framework of the prospect theory contributes to avoiding risk. Especially when the market performs poorly, introducing regime switching information can affect the investment decision, and is beneficial for investors to obtain stable returns. Above all, certain reference meanings can be provided for the risk management of capital market in China and institutional investors and fund managers may be helped hold diversified portfolio.

Key words: prospect theory, hidden Markov model, mixture normal distribution, dynamic stochastic programming