Derivat

a

We will take \(G(P(t),t)\) to figure the price of an option, with \(t\) being time, strike price \(X\) (not introduced yet), and expiration date \(T > t\) on a stock with price \(P(t)\) at time \(t\).

This representation does something really important: it expresses \(G\) as a function of only the current stock price \(P(t)\).

A derived variable is a mapping between states to a set, usually the natural numbers. Remember, if we can, given a state and match it to a number and show a relation which would iterate the state and decrease the states’ number. We can show that the algorithm terminates.