Existence and Uniqueness of Viscosity Solutions of an Integro-differential Equation Arising in Option Pricing

DOI10.1137/20M1341441zbMath1461.91313OpenAlexW3156148599WikidataQ115246895 ScholiaQ115246895MaRDI QIDQ4988556

Hitoshi Ishii, Alexandre F. Roch

Publication date: 17 May 2021

Published in: SIAM Journal on Financial Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m1341441

zbMATH Keywords

maximum principleoption pricingviscosity solutionsmultivariate stochastic volatility model with jumps

Mathematics Subject Classification ID

Stopping times; optimal stopping problems; gambling theory (60G40) Derivative securities (option pricing, hedging, etc.) (91G20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Cites Work

• The Pricing of Options and Corporate Liabilities
• On the definition, stationary distribution and second order structure of positive semidefinite Ornstein-Uhlenbeck type processes
• Viscosity solutions and American option pricing in a stochastic volatility model of the Ornstein-Uhlenbeck type
• The maximum principle for semicontinuous functions
• The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
• Second-order elliptic integro-differential equations: viscosity solutions' theory revisited
• The Black-Scholes equation in stochastic volatility models
• Option pricing with transaction costs and a nonlinear Black-Scholes equation
• A ``maximum principle for semicontinuous functions applicable to integro-partial differential equations
• Integro-differential equations for option prices in exponential Lévy models
• Martingales versus PDEs in finance: an equivalence result with examples
• Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics
• Matrix Subordinators and Related Upsilon Transformations
• Lévy Processes and Stochastic Calculus
• On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's
• User’s guide to viscosity solutions of second order partial differential equations
• Merton's portfolio optimization problem in a Black and Scholes market with non‐Gaussian stochastic volatility of Ornstein‐Uhlenbeck type
• European Option Pricing with Transaction Costs
• Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type
• Option Pricing in Multivariate Stochastic Volatility Models of OU Type
• THE MULTIVARIATE supOU STOCHASTIC VOLATILITY MODEL
• A Non‐Gaussian Ornstein–Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item