  We establish a generalization of Noether theorem for stochastic optimal
control problems. Exploiting the tools of jet bundles and contact geometry, we
prove that from any (contact) symmetry of the Hamilton-Jacobi-Bellman equation
associated to an optimal control problem it is possible to build a related
local martingale. Moreover, we provide an application of the theoretical
results to Merton's optimal portfolio problem, showing that this model admits
infinitely many conserved quantities in the form of local martingales.
