An equilibrium model of debt and bankruptcy

Alberto Bressan, Khai T. Nguyen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We study optimal strategies for a borrower, who services a debt in an infinite time horizon, taking into account the risk of possible bankruptcy. In a first model, the interest rate as well as the instantaneous bankruptcy risk are given, increasing functions of the total amount of debt. In a second model only the bankruptcy risk is given, while the interest rate is determined from a Nash equilibrium, in a game between the borrower and a pool of risk-neutral lenders. This yields a non-standard optimal control problem for the borrower, where the dynamics involves all future values of the control. For this model, optimal repayment strategies are constructed, in open-loop form. In addition, for optimal strategies in feedback form, our analysis shows that the value function should satisfy a new kind of nonlinear, degenerate elliptic equation.

Original languageEnglish (US)
Pages (from-to)953-982
Number of pages30
JournalESAIM - Control, Optimisation and Calculus of Variations
Issue number4
StatePublished - Oct 1 2016

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics


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