Scenario tree generation for multiperiod financial optimization by optimal discretization

Multiperiod financial optimization is usually based on a stochastic model for the possible market situations. There is a rich literature about modeling and estimation of continuous-state financial processes, but little attention has been paid to how to approximate such a process by a discrete-state scenario process and how to measure the pertaining approximation error. In this paper we show how a scenario tree may be constructed in an optimal manner on the basis of a simulation model of the underlying financial process by using a stochastic approximation technique. Consistency relations for the tree may also be taken into account.