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Numerische Mathematik

, Volume 98, Issue 4, pp 607–646 | Cite as

Convergence of numerical schemes for viscosity solutions to integro-differential degenerate parabolic problems arising in financial theory

  • Maya Briani
  • Claudia La Chioma
  • Roberto NataliniEmail author
Article

Summary.

We study the numerical approximation of viscosity solutions for integro-differential, possibly degenerate, parabolic problems. Similar models arise in option pricing, to generalize the celebrated Black–Scholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Convergence is proven for monotone schemes and numerical tests are presented and discussed.

Keywords

Viscosity Numerical Scheme Stock Return Numerical Approximation Viscosity Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgments.

The first two authors would like to thank the whole staff of IAC-CNR for their kind hospitality during the development of this work.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Maya Briani
    • 1
  • Claudia La Chioma
    • 2
  • Roberto Natalini
    • 3
    Email author
  1. 1.Università di Roma “La Sapienza”Dipartimento per le Decisioni Economiche e FinanziarieRomaItaly
  2. 2.Università di Roma “La Sapienza”Dipartimento di Matematica Pura ed ApplicataRomaItaly
  3. 3.Istituto per le Applicazioni del Calcolo “Mauro Picone”Consiglio Nazionale delle RicercheRomaItaly

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