Geometric Brownian distribution of solar radiation with an economic application

Abstract This paper presents the results of a recent model by Hamlen and Hamlen[1] which uses a distributed lag model to predict local levels of incoming solar radiation. The results indicate that the daily levels display a geometric Brownian motion. This distribution was introduced by Professor Samuelson[2] to explain the movement in stock prices over time. It modifies the more familiar arithmetic Brownian motion to eliminate the problem of negative values of the predicted stock prices with a high probability. Solar radiation, kike stock prices, cannot take on negative values and requires the geometric Brownian motion. The distribution is introduced and parameters of the distribution are given for twenty-two cities in the U.S. The results are then applied to the problem of determining economically efficient combinations of heating technologies given a solar heating system and a conventional backup system. A production function for heat is developed that results in a stochastic function with two random variables: available solar radiation and outside temperature. This, in turn, results in a chance constrained cost minimization problem.