In American style exotic options, the holder is often faced with choices at certain times during the life span of the option. Following the/an optimal choice allows the user to maximize the value of the option. The price of the option, in my understanding, comes from assuming the decision that maximizes the conditional expectation of the payoff. How is the delta of such options usually computed? What is the relationship between the delta and the optimal choice at a given time, if there is any?