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Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type
Department of Mathematics, Uppsala University, Sweden.
Department of Mathematics, Uppsala University, Sweden.
Department of Mathematics, Uppsala University, Sweden.
2014 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 193, no 4, 1213-1247 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the system where . A special case of this type of system of variational inequalities with terminal data occurs in the context of optimal switching problems. We establish a general comparison principle for viscosity sub- and supersolutions to the system under mild regularity, growth, and structural assumptions on the data, i.e., on the operator and on continuous functions , , and . A key aspect is that we make no sign assumption on the switching costs and that is allowed to depend on as well as . Using the comparison principle, the existence of a unique viscosity solution to the system is constructed as the limit of an increasing sequence of solutions to associated obstacle problems. Having settled the existence and uniqueness, we subsequently focus on regularity of beyond continuity. In this context, in particular, we assume that belongs to a class of second-order differential operators of Kolmogorov type of the form: where . The matrix is assumed to be symmetric and uniformly positive definite in . In particular, uniform ellipticity is only assumed in the first coordinate directions, and hence, may be degenerate.

Place, publisher, year, edition, pages
Springer, 2014. Vol. 193, no 4, 1213-1247 p.
Keyword [en]
System, Variational inequality, Existence, Viscosity solution, Obstacle problem, Regularity, Kolmogorov equation, Ultraparabolic, Hypoelliptic, Backward stochastic differential equation, Reflected backward stochastic differential equation, Optimal switching problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-65956DOI: 10.1007/s10231-013-0325-yISI: 000339962000017OAI: oai:DiVA.org:umu-65956DiVA: diva2:605314
Available from: 2013-02-13 Created: 2013-02-13 Last updated: 2017-10-12

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Lundström, Niklas L PNyström, Kaj
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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • vancouver
  • Other style
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
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Output format
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  • asciidoc
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