An application of Mellin transform techniques to a black-Scholes equation problem

In this article, we use a Mellin transform approach to prove the existence and uniqueness of the price of a European option under the framework of a Black-Scholes model with time-dependent coefficients. The formal solution is rigorously shown to be a classical solution under quite general European contingent claims. Specifically, these include claims that are bounded and continuous, and claims whose difference with some given but arbitrary polynomial is bounded and continuous. We derive a maximum principle and use it to prove uniqueness of the option price. An extension of the put-call parity which relates the aforementioned two classes of claims is also given.