Controllability and hedgibility of black-scholes equations with n stocks

摘要

This paper is to investigate the controllability and observability properties of linear and certain nonlinear Black-Scholes (B-S) type equations consisting of N stocks in an appropriate bounded domain I of ? _+~N . In this model both the stock volatility and interest rate are influenced by the stock prices and the control which is related to the hedging ratio in option pricing of finance is distributed over a subdomain of I. The proof of the controllability result for the linear B-S equations relies on the suitable observability inequality for the associated adjoint problem, and for the nonlinear model, fixed point technique is applied. Our result leads to that the dynamic hedgibility in finance is proved in the context of controllability theory.