Based On The Optimal Portfolio Under The Same Monotonous Way

This paper puts the comonotonic method into a portfolio choice problem of a saving plan model for the retirement. The so-called comonotonic method means that one finds the comonotonic upper bound and the comonotonic lower bound of the dependent random variables, and then changes the final goal function including these dependent random variables into a comonotonic upper bound function and a comonotonic lower bound function with only one real variable. Thus, one can get the comonotonic upper solution and the comonotonic lower solution to the two corrected models. Considering these random variables are dependent, it makes the non-linear portfolio model hard for us to get the analytical solution. However, if we can get the comonotonic upper solution and the comonotonic lower solution of the portfolio model, it will do a lot to the final solution of the problem, and this is the importance of the comonotonic method.With the comonotonic method, the paper solves the problems in the discrete-time case and the continuous-time case, and gets some interesting results.Firstly, we construct a specific model in the discrete-time case, and then get the comonotonic upper solution and the comonotonic lower solution by virtue of the comonotonic method.Next, we also give the specific model in the continuous-time case similar to the discrete-time setting, and then get the comonotonic upper solution and the comonotonic lower solution by using the same argument.