Positive solutions of a Dirichlet problem for a stationary nonlinear Black-Scholes equation

DOI10.1016/J.NA.2009.03.026zbMath1175.35050OpenAlexW1970869467MaRDI QIDQ838065

F. Fabião, Maria do Rosário Grossinho, Onofre Alves Simões

Publication date: 21 August 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.03.026

zbMATH Keywords

stochastic volatilityupper and lower solutionsstationary solutionsBlack-Scholes equationexistence and localization

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Auctions, bargaining, bidding and selling, and other market models (91B26) Variational methods for second-order elliptic equations (35J20)

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Cites Work

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• Solutions to a stationary nonlinear Black-Scholes type equation
• A Risk-Neutral Stochastic Volatility Model
• Existence of stable periodic solutions of a semilinear parabolic problem under Hammerstein-type conditions
• Solvability of the Dirichlet-periodic problem for a nonlinear parabolic equation under conditions on the potential

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