Solutions to a gradient-dependent integro-differential parabolic problem arising in the pricing of financial options in a Lévy market

DOI10.1016/j.jmaa.2011.06.029zbMath1227.35144OpenAlexW2033120229MaRDI QIDQ641552

Marc Salas, Maria Christina Mariani, Indranil SenGupta

Publication date: 24 October 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.06.029

zbMATH Keywords

existence of solutionsArzelà-Ascoli theoremprocess with jumps

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Microeconomic theory (price theory and economic markets) (91B24) Semilinear parabolic equations (35K58) Integro-partial differential equations (35R09)

Related Items (4)

Option Pricing with Transaction Costs and Stochastic Interest Rate ⋮ Numerical methods applied to option pricing models with transaction costs and stochastic volatility ⋮ On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models ⋮ Spherical harmonics applied to differential and integro-differential equations arising in mathematical finance

Cites Work

• The Pricing of Options and Corporate Liabilities
• Jump-diffusion processes: volatility smile fitting and numerical methods for option pricing
• Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
• Spectral analysis for a three-dimensional superradiance problem
• Second-order elliptic integro-differential equations: viscosity solutions' theory revisited
• Differential operator related to the generalized superradiance integral equation
• Integro-differential equations for option prices in exponential Lévy models
• A parabolic problem arising in financial mathematics
• Computing the implied volatility in stochastic volatility models
• Stochastic Volatility: Option Pricing using a Multinomial Recombining Tree
• A uniqueness theorem for a class of non-classical parabolic equations
• A Risk-Neutral Stochastic Volatility Model
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Equivalent Norms for Sobolev Spaces
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