
Minimax Theory and its Applications 05 (2020), No. 2, 251274 Copyright Heldermann Verlag 2020 A Model of Debt with Bankruptcy Risk and Currency Devaluation Rossana Capuani Dept. of Mathematics, North Carolina State University, Raleigh, NC 27695, U.S.A. rcapuan@ncsu.edu Steven Gilmore Dept. of Mathematics, North Carolina State University, Raleigh, NC 27695, U.S.A. sjgilmo2@ncsu.edu Khai T. Nguyen Dept. of Mathematics, North Carolina State University, Raleigh, NC 27695, U.S.A. khai@math.ncsu.edu The paper studies a system of HamiltonJacobi equations, arising from a stochastic optimal debt management problem in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of riskneutral lenders. In this model, the borrower is a sovereign state that can decide how much to devaluate its currency and which fraction of its income should be used to repay the debt. Moreover, the borrower has the possibility of going bankrupt at a random time and must declare bankruptcy if the debt reaches a threshold x*. When bankruptcy occurs, the lenders only recover a fraction of their capital. To offset the possible loss of part of their investment, the lenders buy bonds at a discounted price which is not given a priori. This leads to a nonstandard optimal control problem. We establish an existence result of solutions to this system and in turn recover optimal feedback payment strategy u*(x) and currency devaluation v*(x). In addition, the behavior of (u*,v*) near 0 and x* is studied. Keywords: Debt management and bankruptcy, optimal feedback solution, stochastic optimal control. MSC: 49J15; 49N90, 91G80, 91B50. [ Fulltextpdf (171 KB)] for subscribers only. 