TY - JOUR

T1 - The vanishing viscosity limit for a system of H-J equations related to a debt management problem

AU - Bressan, Alberto

AU - Jiang, Yilun

N1 - Funding Information:
2010 Mathematics Subject Classification. Primary: 34B15, 35Q91, 49N70, 91A23. Key words and phrases. Vanishing viscosity, discontinuous feedback control, debt management. This research was partially supported by NSF, with grant DMS-1411786: Hyperbolic Conservation Laws and Applications.
Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All rights reserved.

PY - 2018/10

Y1 - 2018/10

N2 - 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.

AB - 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.

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U2 - 10.3934/dcdss.2018050

DO - 10.3934/dcdss.2018050

M3 - Article

AN - SCOPUS:85053710790

SN - 1937-1632

VL - 11

SP - 793

EP - 824

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 5

ER -