Kybernetika 44 no. 5, 685-704, 2008

On exact null controllability of Black-Scholes equation

Kumarasamy Sakthivel, Krishnan Balachandran, Rangarajan Sowrirajan and Jeong-Hoon Kim


In this paper we discuss the exact null controllability of linear as well as nonlinear Black-Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with $L^2$ topology.