  The paper studies a system of first order Hamilton-Jacobi equations with
discontinuous coefficients, arising from a model of deterministic optimal debt
management in infinite time horizon, with exponential discount and currency
devaluation. The existence of an equilibrium solution is obtained by a suitable
concatenation of backward solutions to the system of Hamilton-Jacobi equations.
A detailed analysis of the behavior of the solution as the debt-ratio-income
$x^*\to +\infty$ is also provided.
