The author presents a new model for stock price fluctuations based on a concept of "information." In contrast, the usual Black-Scholes-Merton-Samuelson (1965, 1973) model is based on the explicit assumption that information is uniformly held by everyone and plays no role in stock prices. The new model is based on the evident nonuniformity of information in the market and the evident time delay until new information becomes generally known. A second contribution of the paper is to present some problems with explicit solutions which are of value in obtaining insights. Several problems of mathematical interest are compared in order to better understand which optimal stopping problems have explicit solutions