Optimal control of a continuous-in-time financial model

The achievement of a project requires tools to monitor and adjust its evolution over time. Rather than to check at mid-term whether the objectives will be achieved or not, and adjust them, it is interesting to develop a control tool in order to effectively conduct the project's objectives. In this paper, we improve the continuous-in-time financial model developed in [Frenod & Chakkour], that describes working of loan and repayment, in order to prepare its capability to be used in control theory approach. The aim is to determine the optimal loan schedule taking into account the objective of the project, the income and the spending. For that, we set out an optimal control method for the strategy elaboration phase to better adjust the project implementation.