An iterative procedure for solving integral equations related to optimal stopping problems∗

We present an iterative algorithm for computing values of optimal stopping problems for one-dimensional diffusions on finite time intervals. The method is based on a time discretisation of the initial model and a construction of discretised analogues of the associated integral equation for the value function. The proposed iterative procedure converges in a finite number of steps and delivers in each step a lower or an upper bound for the discretised value function on the whole time interval. We also give remarks on applications of the method for solving the integral equations related to several optimal stopping problems.