Fachvortrag in englischer Sprache

In an optimal stopping problem (in discrete time), a person can decide at each time step either to stop a given system or to continue the system. The person receives some amount of money depending on the state of the system at the time the system is stopped, and the goal is to maximize the expected reward by choosing an optimal stopping time. In mathematical finance optimal stopping problems describe the price of options with early exercise features such as American options and Bermudan options. Here the payoff for exercising the option (i.e. stopping the system) may depend on a high-dimensional vector of underlying variables such as interest rates over different periods of time. Motivated by this type of application, a rich literature on Monte Carlo methods for high-dimensional optimal stopping problems was developed during the last decade. In this talk we will survey some of these algorithms with a focus on the construction of confidence intervals for the value of the optimal stopping problem, which corresponds to the price of the early exercise option in the financial application. Advantages and drawbacks of the different approaches are illustrated by numerical examples on option pricing in interest rate markets.

Speaker: Prof. Dr. Christian Bender, Saarland University