Stopping Problems in Finance

Abstract

Typical stopping problems in finance involve the pricing of American options. It can be shown by using no-arbitrage arguments that the price of an American option is the value of an optimal stopping problem under a risk neutral probability measure and the optimal stopping time is the optimal exercise time of the option. In order to have a complete financial market without arbitrage we restrict the first section on pricing American options to the binomial model. An algorithm is presented for pricing American options and the American put option is investigated in detail. In particular also perpetual American put options are studied. In Section 11.2 so-called credit granting problems are considered. Here the decision maker has to decide whether or not a credit is extended. In this context, a Bayesian Model is also presented.