Optimal Trading Using Black-Scholes Equation with Transaction Costs

Abstract

This work deals with optimal trading using Black-Scholes equation with transaction costs. The partial differential equation for option pricing with transaction costs on the domain (P,T)∈(0,∞)×(0,T) with terminal condition C(P,T)=Max(P-E,0),P∈(0,∞) for European call options with strike price, E, and a suitable terminal condition for European puts was obtained and then solved to obtain the optimal value function.