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

Authors:
Maya Briani;Claudia La Chioma;Roberto Natalini
Affiliations:
Dipartimento per le Decisioni Economiche e Finanziarie, Università di Roma “La Sapienza”, Via del Castro Laurenziano, 00161, Roma, Italy;Dipartimento di Matematica Pura ed Applicata, Università di Roma “La Sapienza”, Piazzale Aldo Moro, 2, 00161, Roma, Italy;Consiglio Nazionale delle Ricerche, Istituto per le Applicazioni del Calcolo “Mauro Picone”, Viale del Policlinico, 137, 00161, Roma, Italy
Venue:
Numerische Mathematik
Year:
2004

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Abstract

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.