Controllability and hedgibility of Black-Scholes equations with \(N\) stocks

DOI10.1007/s10440-009-9548-8zbMath1198.91213OpenAlexW2062546381MaRDI QIDQ983690

J. Martínez

Publication date: 24 July 2010

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-009-9548-8

zbMATH Keywords

observabilitycontrollabilityinitial boundary value problemvolatilityBlack-Scholes equationssecond order differential operatorhedgibility

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Optimal stochastic control (93E20) Derivative securities (option pricing, hedging, etc.) (91G20) Existence of optimal solutions to problems involving randomness (49J55)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Pricing of Options and Corporate Liabilities
• Exact controllability to trajectories for a semilinear heat equation with a superlinear nonlinearity
• Compact sets in the space \(L^ p(0,T;B)\)
• Exact controllability of the superlinear heat equation
• Local controllability of the phase field system
• A Black--Scholes option pricing model with transaction costs
• Local exact controllability of a reaction-diffusion system
• Solutions to a stationary nonlinear Black-Scholes type equation
• Carleman estimates for coefficient inverse problems and numerical applications.
• Exact local controllability of a one-control reaction-diffusion system
• Existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets
• On the regularity of the free boundary in the parabolic obstacle problem. Application to American options
• Far Field Boundary Conditions for Black--Scholes Equations
• Optimal and near-optimal advection—diffusion finite-difference schemes III. Black—Scholes equation
• Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets
• Contróle Exact De Léquation De La Chaleur
• A nonlinear partial differential equation for american options in the entire domain of the state variable
• The Mathematics of Financial Derivatives
• Null controllability of nonlinear convective heat equations
• Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates
• Arbitrage Theory in Continuous Time