The present thesis successfully solved three innovative optimal control problems in a high-frequency trading market environment: liquidation, acquisition, and market-making. We optimized and produced general solutions applicable to any stochastic differential equation representing a price with drift and diffusion parameters. Our cases of study for price processes were the Markov Process (MP), the Semi-Markov Process (SMP) and General Compound Hawkes Process (GCHP). For these three optimized models, the Agent maximizes their utility or value function by solving the Hamilton-Jacobi-Bellman (HJB) equation and designing a strategy for asset trading. The results showed to be sensitive to the parameters of the diffusion process driving the prices, inheriting essential price characteristics to be reflected in the trading strategy. The optimal solutions were expressed based on the parameters to model the market, the stock and the Agent. We visualized and analyzed the LOBSTER data to facilitate a better understanding of the models, where we calibrated the parameters for the three optimal control problems by doing an extensive numerical exercise and comparing the solutions among the cases MP, SMP and GCHP. The implementation and comparison of the optimized Liquidation, Acquisition and Market-Making models showed the potential to optimize the Agent’s wealth and how each model can have better outcomes with different price models, according to the managed stock. In conclusion, the regular operation of the solutions for the optimal Liquidation, Acquisition and Market-Making with a proper price SDE model gives the Agent a complete trading strategy to participate promptly and wisely in a High-Frequency Trading market. The application of the solutions to these optimal control problems would make a difference in the expected income of the Agent in the short and long run.