Abstract: In Black-Scholes type financial markets,the CaR dynamic portfolio decision model with constraint of investment chance is established as following: , where x is the initial wealth,P(t=(P₁(t),,,P_d(t)c I R^d is the process of feasible portfolio,X^P(T)is the terminal wealth, R is a positive wealth level given by investor and 0<β<1.The explicit solutions for this model are obtained in terms of the optimal constant rebalance strategy.The financial interpretations of the results include that,for portfolio decision with constraint of investment chance,the optimal constant rebalance strategy is pure bond investment strategy and the optimal Capital-at-Risk is zero in neutral risk markets,and the optimal constant rebalance strategy implies the mutual fund theorem in non-neutral risk markets.

Key words: Capital-at-Risk(CaR), constraint of investment chance, dynamic portfolio, constant rebalance strategy