The authors analyze, in a Black-Scholes framework, relations between American options prices and European options prices. They exhibit a large class of payoffs
for which the American option price
has a closed-form expression. The main theorem is Theorem 3. Let
is the European option price for a payoff
. Theorem 3 gives conditions on
to insure that
has to verify
. Examples verifying Theorem 3 hypotheses are given.