STOCHASTIC EQUILIBRIUM SOLUTION FOR A DEBT MANAGEMENT PROBLEM WITH CURRENCY DEVALUATION

Consider a model of debt management, where a sovereign state trades some bonds to service the debt with a pool of risk-neutral competitive foreign investors. At each time, the government decides which fraction of the gross domestic product (GDP) should be used to repay the debt, and how much to devaluate its currency. Both these operations have the effect to reduce the actual size of the debt, but have a social cost in terms of welfare sustainability. When the debt-to-GDP ratio reaches a given size x*, bankruptcy instantly occurs. Moreover, at any time the sovereign state can declare bankruptcy by paying a correspondent bankruptcy cost. To offset the possible loss of part of their investment, the foreign investors buy bonds at a discounted price which is not given a priori. This leads to a nonstandard optimal control problem. For a given bankruptcy threshold x*, we show that the optimization problem admits an equilibrium solution. The paper also studies properties of optimal feedback strategies, and the asymptotic behaviour of the expected total cost to the borrower as x* is pushed to infinity.