In quantitative finance, there are many new aspects and developments related to the stochastic control and optimization problems which studies the controlled variables performing the behaviour of a dynamical system to achieve an aim. In this talk, we consider the optimal limit and market orders for high-frequency trading. First, we work on the stochastic control problem and the associated Hamilton-Jacobi-Bellman (HJB) partial differential equation by maximizing the expected utility. Then, we find the optimal bid and ask prices by solving the related HJB equation. Finally, we make some conclusions on the market maker’s performance where these optimal prices are used on trading by some simulation results.