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Using mathematical approaches to optimally manage public debt

In this model, governments face two opposing costs. On the one hand, they aim to minimize the total expected opportunity cost due to debt. This may result, for instance, from private investment crowding out public investments, leaving less room for public ventures, and from a tendency to suffer low subsequent growth. On the other hand, by reducing the debt through, say, fiscal policies, the government incurs a cost that is proportional to the amplitude of its action. It is important for governments to properly counterbalance these two costs, and such a problem can be modeled mathematically through a so-called singular stochastic control problem.