The vanishing viscosity limit for a system of H-J equations related to a debt management problem

Alberto Bressan, Yilun Jiang

Research output: Contribution to journalArticle

Abstract

The paper studies a system of Hamilton-Jacobi equations, arising from a model of optimal debt management in infinite time horizon, with exponential discount and a bankruptcy risk. For a stochastic model with positive diffiusion, the existence of an equilibrium solution is obtained by a topological argument. Of particular interest is the limit of these viscous solutions, as the diffiusion parameter approaches zero. Under suitable assumptions, this (possibly discontinuous) limit can be interpreted as an equilibrium solution to a non-cooperative differential game with deterministic dynamics.

Original languageEnglish (US)
Pages (from-to)793-824
Number of pages32
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume11
Issue number5
DOIs
StatePublished - Oct 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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