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

Alberto Bressan; Yilun Jiang

doi:10.3934/dcdss.2018050

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

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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 language	English (US)
Pages (from-to)	793-824
Number of pages	32
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	11
Issue number	5
DOIs	https://doi.org/10.3934/dcdss.2018050
State	Published - Oct 2018

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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Bressan, A., & Jiang, Y. (2018). The vanishing viscosity limit for a system of H-J equations related to a debt management problem. Discrete and Continuous Dynamical Systems - Series S, 11(5), 793-824. https://doi.org/10.3934/dcdss.2018050

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