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 language||English (US)|
|Number of pages||32|
|Journal||Discrete and Continuous Dynamical Systems - Series S|
|State||Published - Oct 2018|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics