A fast preconditioned policy iteration method for solving the tempered fractional HJB equation governing American options valuation

DOI10.1016/j.camwa.2017.02.040zbMath1372.91115OpenAlexW2601947471MaRDI QIDQ2403726

Siu-Long Lei, Xu Chen, Deng Ding, Wen-Fei Wang

Publication date: 12 September 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.02.040

zbMATH Keywords

Hamilton-Jacobi-Bellman equationunconditional stabilityAmerican optionspreconditionertempered fractional derivative

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stopping times; optimal stopping problems; gambling theory (60G40) Derivative securities (option pricing, hedging, etc.) (91G20)

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Uses Software

• TFPDE

Cites Work

• The Pricing of Options and Corporate Liabilities
• A Jump-Diffusion Model for Option Pricing
• A penalty method for a fractional order parabolic variational inequality governing American put option valuation
• Preconditioned iterative methods for fractional diffusion equation
• Tempered fractional calculus
• A circulant preconditioner for fractional diffusion equations
• Multigrid method for fractional diffusion equations
• A predictor-corrector approach for pricing American options under the finite moment log-stable model
• M-matrix characterizations. I: nonsingular M-matrices
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• A fast preconditioned penalty method for American options pricing under regime-switching tempered fractional diffusion models
• A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
• The numerical simulation of the tempered fractional Black-Scholes equation for European double barrier option
• An upwind finite difference method for a nonlinear Black-Scholes equation governing European option valuation under transaction costs
• Quadratic Convergence for Valuing American Options Using a Penalty Method
• Pricing American options under multi-state regime switching with an efficientL- stable method
• Circulant preconditioning technique for barrier options pricing under fractional diffusion models
• Preconditioned iterative methods for fractional diffusion models in finance
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Some mathematical results in the pricing of American options
• Numerical methods for dynamic Bertrand oligopoly and American options under regime switching
• Fast solution algorithms for exponentially tempered fractional diffusion equations
• On the Use of Policy Iteration as an Easy Way of Pricing American Options
• Comparison and survey of finite difference methods for pricing American options under finite activity jump-diffusion models
• High Order Algorithms for the Fractional Substantial Diffusion Equation with Truncated Lévy Flights
• Numerical Methods for SPDEs with Tempered Stable Processes
• Penalty methods for continuous-time portfolio selection with proportional transaction costs
• An Introduction to Iterative Toeplitz Solvers
• Accurate Evaluation of European and American Options Under the CGMY Process
• Option pricing when underlying stock returns are discontinuous
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