Based on a dynamic model of the stochastic repayment behavior exhibited by delinquent credit-card accounts as a self-exciting point process, a bank can control the arrival intensity of repayments using costly account-treatment actions. A semi-analytic solution to the corresponding stochastic optimal control problem is obtained using a recursive approach. For an affine cost of treatment interventions, the optimal policy in the two-dimensional (intensity, balance)-space is described by the frontier of the connected (but nonconvex) action region. The optimal policy significantly reduces a bank's loss given default and concentrates the collection effort onto the best possible interventions at the best possible times, so as to minimize the sum of the expected discounted outstanding balance and the discounted cost of the collection effort, thus maximizing the net value of any given delinquent credit-card account.