We study the constant discount rate present value model for stock pricing in a stochastic setting where the exogenous dividend stream is modeled as a random walk with innovations drawn from the family of stable distributions. We derive an exact analytical solution for the fundamental stock price. We evaluate the ability of the model fundamentals and the dividends-driven intrinsic bubbles to explain the observed variation in annual U.S. stock prices. We compare results obtained in this setting with those from the traditional model where all stochastic processes are driven by Gaussian shocks.

A group of n susceptible individuals exposed to a contagious disease is considered. It is assumed that at each instant in time one or more susceptible individuals can contract the disease.

The progress of this epidemic is modeled by a stochastic process Xn (t), t in [0,∞) representing the number of infective individuals at time t. It is shown that Xn (t), with the suitable standardization and under a mild condition, converges in distribution as n → ∞to a normal random variable for all t in (0, t 0), where t 0 is an identifiable number.