In recent years various suggestions have been made how to price European-type contingent claims in incomplete markets. By contrast, there is only little corresponding literature dealing with American options in incomplete markets.
Therefore, in the first part of the talk the neutral valuation approach is applied to American and game options. Neutral prices occur if investors are utility maximizers and if derivative supply and demand are balanced. A game option (also referred to as Israeli option or recall option) is a generalization of an American option which also enables the seller to terminate it before maturity, but at the expense of a penalty. Then, we present a Monte Carlo valuation approach for game options similar to Rogers (2002) (joint work with Jan Kallsen and Andreas Kyprianou).