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The paper studies a system of first order Hamilton-Jacobi equations withdiscontinuous coefficients, arising from a model of deterministic optimal debtmanagement in infinite time horizon, with exponential discount and currencydevaluation. The existence of an equilibrium solution is obtained by a suitableconcatenation 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.

Solutions to a system of first order H-J equations related to a debt management problem