INTEGRAL REPRESENTATION OF THE SOLUTION TO A NONLINEAR BLACK–SCHOLES EQUATION WITH TRANSACTION COSTS

Abstract

This paper addresses a nonlinear partial differential equation (PDE) derived from a modified option pricing model incorporating transaction costs, as described in the works of [2], [4], [5], and [6]. The equation is reduced to the classical heat equation via a logarithmic transformation and an appropriate substitution. An integral representation of the solution is derived at a mathematical justification provided for the transformation. Formal results are presented in the form of lemmas, propositions, and theorems. The solution obtained can be used to price a European call option.