APPLICATION OF FIXED POINT THEOREM TO EXISTENCE OF THE SOLUTION OF BLACK-SCHOLES PARTIAL DIFFERENTIAL EQUATION IN SOBOLEV SPACE
BRIGHT O. OSU *
Department of Mathematics, Abia State University, Uturu, Nigeria
CHIDINMA OLUNKWA
Department of Mathematics, Abia State University, Uturu, Nigeria
*Author to whom correspondence should be addressed.
Abstract
In this paper, we discuss the existence of solution of nonlinear Black-Scholes partial differential equation with transaction cost and volatile portfolio risk measure of the type;
In Sobolev space using fixed point theorem.
Keywords: Black-Scholes differential equation, sobolev space, fixed point theorem, holomorphic function