This paper proposes a deep learning algorithm for solving stochastic control problems, with a focus on the utility maximisation problem. The algorithm solves Markovian problems via the Hamilton Jacobi Bellman (HJB) equation. We solve this highly nonlinear partial differential equation (PDE) with a second order backward stochastic differential equation (2BSDE) formulation. The convex structure of the problem allows us to describe a dual problem that can either verify the original primal approach or bypass some of the complexity. We apply the algorithm to problems with power, log and non-HARA utilities in the Black-Scholes model. Numerical experiments show highly accurate results with low computational cost, supporting our proposed algorithm.