Optimal portfolio of continuous-time mean-variance model with futures and options

This paper is concerned with the portfolio selection of options that have different sale and purchase prices based on the continuous-time mean-variance criterion in financial markets. The optimal investment problem is formulated as a continuous-time mathematical model. These price processes follow jump-diffusion processes (the Weiner process and the Poisson process). With the theory of stochastic linear-quadratic control and viscosity solutions, the corresponding Hamilton-Jacobi-Bellman equation of the problem is represented and its solutions are obtained in different conditions. The optimal investment strategies are presented. In addition, the efficient frontier is also illustrated. Finally, an example and some discussions illustrating these results are also presented.