We consider a spread financial market defined by the Ornstein–Uhlenbeck (OU) process with a diffusion coefficient driven by a stochastic differential equation.For this market we study the optimal consumption/investment problem under logarithmic utilities. This problem is studied on the base of the stochastic dynamical programming approach.To this end we show aspecial verification theorem for this case.Then, we study the corresponding Hamilton–Jacobi–Bellman (HJB) equation and find its solution in explicit form.Finally,through this solution we construct the optimal financial strategies.