Exact null controllability of a semilinear parabolic equation arising in finance

This paper is concerned with the exact null controllability of certain semilinear Black–Scholes type equations in a bounded interval of R+R+ with Neumann boundary conditions. The control is assumed to be distributed along a subset ωω of II. First, we prove the exact null controllability of an associated linearized problem by establishing the observability estimate derived from a Carleman type inequality which is the key result for the whole theory. Then, the exact null controllability of the nonlinear problem is discussed using the infinite-dimensional Kakutani fixed point theorem.