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

Abstract

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 $x^{\ast }\to +\infty$ is also provided.

35. arXiv admin note: substantial text overlap with arXiv:1805.05043