Variational inequalities and the pricing of American options

This paper is devoted to the derivation of some regularity properties of pricing functions for American options and to the discussion of numerical methods, based on the Bensoussan-Lions methods of variational inequalities. In particular, we provide a complete justification of the so-called Brennan-Schwartz algorithm for the valuation of American put options.Research supported in part by a contract from Banque INDOSUEZ.