# Optimal Expected Value of Assets Under Black-Scholes Equation with Transaction Costs Joy Ijeoma Adindu-Dick

**Abstract: ** This paper deals with optimal expected value of assets under Black-Scholes equation with transaction costs. The partial differential equation for option pricing with transaction costs on the domain $(P,T)\in(0,\infty)\times (0,T)$ with terminal condition $C(P,T)=max(P-E,0),P\in(0,\infty)$ for European call options with strike price $E$, and a suitable terminal condition for European puts was obtained and then solved using Euler’s substitution method.

**Keywords: **Black-Scholes equation with transaction costs, Optimal value, Euler’s substitution method, Option pricing.

**How to cite this article:**

Joy Ijeoma Adindu-Dick, Optimal Expected Value of Assets Under Black-Scholes Equation with Transaction Costs, International Journal of Advances in Mathematics, Volume 2018, Number 3, Pages 17-24, 2018.