A PDE approach to regularity of solutions to finite horizon optimal switching problems

T. Arnarson; B. Djehiche; M. Poghosyan; H. Shahgholian

doi:10.1016/j.na.2009.05.063

A PDE approach to regularity of solutions to finite horizon optimal switching problems

T. Arnarson, B. Djehiche, M. Poghosyan, H. Shahgholian

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C^{1, 1}-regular away for the free boundaries of the action sets.

Original language	English (US)
Pages (from-to)	6054-6067
Number of pages	14
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	71
Issue number	12
DOIs	https://doi.org/10.1016/j.na.2009.05.063
State	Published - Dec 15 2009

Keywords

Backward stochastic differential equation
Default risk
Optimal switching
Real options
Security design
Snell envelope
Stopping and starting
Stopping time
Variational inequalities
Viscosity solution of PDEs

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2009.05.063

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abstract = "We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C1, 1-regular away for the free boundaries of the action sets.",

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AU - Arnarson, T.

AU - Djehiche, B.

AU - Poghosyan, M.

AU - Shahgholian, H.

PY - 2009/12/15

Y1 - 2009/12/15

N2 - We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C1, 1-regular away for the free boundaries of the action sets.

AB - We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C1, 1-regular away for the free boundaries of the action sets.

KW - Backward stochastic differential equation

KW - Default risk

KW - Optimal switching

KW - Real options

KW - Security design

KW - Snell envelope

KW - Stopping and starting

KW - Stopping time

KW - Variational inequalities

KW - Viscosity solution of PDEs

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 12

ER -

A PDE approach to regularity of solutions to finite horizon optimal switching problems

Abstract

Keywords

ASJC Scopus subject areas

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