This paper deals with the mathematical model of managing an employee’s professional profile formation by the employer. It is based on the optimal stopping theory for a continuous time stochastic processes [see G. Peskir and A. Shiryaev, Optimal stopping and free-boundary problems. Lectures in Mathematics, ETH Zürich. Basel: Birkhäuser (2006; Zbl 1115.60001); I. Karatzas and S. E. Shreve, Methods of mathematical finance. Applications of Mathematics. Berlin: Springer (1998; Zbl 0941.91032)] with finite horizon.
The authors continue the investigation from their articles [Panam. Math. J. 18, No. 3, 1–13 (2008; Zbl 1149.60023)] (a discrete-time framework) and [Far East J. Appl. Math. 33, No. 1, 121–140 (2008; Zbl 1153.91486)] (where specific numerical examples are presented). The problem of optimal stopping the discounted process \((\tilde{Z}_t)_{t\in\overline{0,T}}\) representing the possible profit when the educational activities are stopped at time \(\tau\in[0,T]\) is solved by the classical method of constructing Snell’s envelope. Using the Doob’s decomposition of the Snell’s envelope it is shown the existence of a self-financing strategy of hedging.