Optimal Stopping Time of a Portfolio Selection Problem with Multi-assets

In this work, we study a right time for an investor to stop the investment among multi-assets over a given investment horizon so as to obtain maximum profit. We formulate it to a two-stage problem. The main problem is not a standard optimal stopping problem due to the non-adapted term in the objective function, and we turn it to a standard one by stochastic analysis. The subproblem with control variable in the drift and volatility terms is solved first via stochastic control method. A numerical example is presented to illustrate the efficiency of the theoretical results.