Short Communication: Mean-Stochastic-Dominance Portfolio Selection in Continuous Time

We examine the mean-stochastic-dominance portfolio selection in a continuous-time market. We establish the sufficient and necessary conditions for the finiteness of the optimal value and the existence of an optimal solution. In the case of existence of the optimal solutions, they are explicitly characterized. In the case of nonexistence of the optimal solutions, an asymptotically optimal solution is provided. This work is complementary to the expected utility maximization problem with stochastic dominance constraints in Wang and Xia [SIAM J. Financial Math., 12 (2021), pp. 1054-1111].