Let $C^E$, $P^E$, $C^A$, and $P^A$ denote prices of a European call option, a European put option, an American call option and an American put option, respectively. All of them with expiry time $T$ and the same strike price $K$. we assume $r\geq 0$ to be the continuously compounded interest rate. I want to show that if it holds that,
then we can make a sure risk-less profit.
Furthermore, I am interested in showing that,
then we can also make a sure risk-less profit.
Anybody have an idea?