Public debt management and tax evasion

This paper deals with the optimal management of the public debt-to-GDP ratio. We specifically focus on a contrasting tax evasion-based strategy for controlling the debt-to-GDP ratio. Two devices can be employed by the policymaker: by the one side, the tax rate is to be applied to the tax payers; by the other side, the monitoring activity is to be performed in order to detect the evaded taxes. To pursue our scopes, a stochastic control problem is developed and solved. Some numerical experiments validate the theoretical proposal and lead to an intuitive discussion of the obtained findings.