A system of first order Hamilton–Jacobi equations related to an optimal debt management problem

The paper studies a system of first order Hamilton–Jacobi equa- tions with discontinuous coefficients, arising from a model of deterministic optimal debt management in infinite time horizon, with exponential dis- count and currency devaluation. The existence of an equilibrium solution is obtained by a suitable concatenation of backward solutions to the sys- tem of Hamilton–Jacobi equations. A detailed analysis of the behavior of the solution as the debt-ratio-income tends to infinity is provided.