The First Passage Time and the Dividend Value Function for One-Dimensional Diffusion Processes between Two Reflecting Barriers

الملخص EN

We consider the general one-dimensional time-homogeneous regular diffusion process between two reflecting barriers.

An approach based on the Itô formula with corresponding boundary conditions allows us to derive the differential equations with boundary conditions for the Laplace transform of the first passage time and the value function.

As examples, the explicit solutions of them for several popular diffusions are obtained.

In addition, some applications to risk theory are considered.