Continuous time one-dimensional asset-pricing models with analytic price-dividend functions
This paper describes a continuous time one-dimensioal asset pricing model by a second-order linear ordinary differential equation which represents equilibrium or a no-arbitrage condition within the economy. If the discount factor and dividend process are analytic, the resulting differential equation has analytic coefficients. Under these circumstances, the one-dimensional Cauchy-Kovalevsky theorem can be used to prove that the solution to such an asset-pricing model is analytic. Also, this theorem allows for the development of a recursive rule, which speeds up the computation of an approximate solution. This theorem yields a uniform bound on the errror in the numerical solution. The Cauchy-Kovalevsky theorem yields a quick and accurate solution of many known asset-pricing models.
continuous time one-dimensional asset pricing model
second-order linear ordinary differential equation
scientific article; zbMATH DE number 5673390