Some weak self-adjoint Hamilton-Jacobi-Bellman equations arising in financial mathematics

In Gandarias (2011) 12] one of the present authors has introduced the concept of weak self-adjoint equations. This definition generalizes the concept of self-adjoint and quasi self-adjoint equations that were introduced by Ibragimov (2006) 11]. In this paper we find a class of weak self-adjoint Hamilton-Jacobi-Bellman equations which are neither self-adjoint nor quasi self-adjoint. By using a general theorem on conservation laws proved in Ibragimov (2007) 9] and the new concept of weak self-adjointness (Gandarias, 2011) 12] we find conservation laws for some of these partial differential equations.