We consider a stylized core-periphery financial network in which links lead to the creation of projects in the outside economy but make banks prone to contagion risk. The controller seeks to maximize, under budget constraints, the value of the financial system defined as the total number of projects. Under partial information on interbank links, revealed in conjunction with the spread of contagion, the optimal control problem is shown to become a Markov decision problem. We determine the optimal intervention policy by using dynamic programming. Our numerical results show that the value of the system depends on the connectivity in a nonmonotonous way: it first increases with connectivity and then decreases with connectivity. The maximum value attained depends critically on the budget of the controller. Moreover, we show that for highly connected systems, it is optimal to increase the rate of intervention in the peripheral banks rather than in core banks.