We present a new method for solving asset pricing models, which yields an analytic price-dividend function of one state variable. To illustrate our method we give a detailed analysis of Abel's asset pricing model. A function is analytic in an open interval if it can be represented as a convergent power series near every point of that interval. In addition to allowing us to solve for the exact equilibrium price-dividend function, the analyticity property also lets us assess the accuracy of any numerical solution procedure used in the asset pricing literature. Copyright The Econometric Society 2005.