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

TL;DR

This paper analyzes a system of Hamilton-Jacobi equations with discontinuities, modeling optimal debt management over infinite time, and establishes the existence of equilibrium solutions along with their asymptotic behavior.

Contribution

It introduces a method to prove the existence of equilibrium solutions for a complex H-J system with discontinuous coefficients in debt management models.

Findings

Existence of equilibrium solutions established.

Detailed asymptotic analysis as debt ratio tends to infinity.

Handling of discontinuous coefficients in H-J equations.

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 $x^*\to +\infty$ is also provided.