An Analytical Approach to Merton’s Rational Option Pricing Theory

In the early 70s Merton developed a theory based on economic arguments to study the properties of option and warrant prices. The main tool in his proofs was the portfolio dominance principle. In the context where the price of a contingent claim satisfies a partial differential equation we provide analytical proofs of Merton’s rational option pricing theory. We use several versions of the maximum principle as well as the sliding and the moving planes methods to prove our results. Our approach enables us to extend the theory to nonlinear models.