The price of stock at time t will be denoted by S(t). It is assumed to be strictly positive for all t. We take t = 0 to be the present time, S(0) being the current stock price, known to all investors. The future prices S(t) for t > 0 remain unknown, in general. Mathematically, S(t) can be represented as a positive random variable on a probability space Ω, that is