Abstract
Under the no-arbitrage condition, the pricing (or evaluation of the fair price) of an American derivative is reduced to an optimal stopping problem under a risk neutral (or an equivalent martingale) probability measure, which involves various interesting problems related to several fields of mathematical sciences. In this article, first, we briefly explain the main principles of this risk neutral evaluation method in the framework of Black-Scholes (-Merton) market. And, then, we present several classical and recently derived results concerning the analytical characterizations of the optimal value function and optimal stopping time, which are useful for its both analytical and numerical evaluation.
