Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation
SIAM Journal on Numerical Analysis
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
SIAM Journal on Numerical Analysis
Linear Complexity Solution of Parabolic Integro-differential Equations
Numerische Mathematik
Accurate Evaluation of European and American Options Under the CGMY Process
SIAM Journal on Scientific Computing
A Finite Element Like Scheme for Integro-Partial Differential Hamilton-Jacobi-Bellman Equations
SIAM Journal on Numerical Analysis
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We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Lévy (jump-diffusion) processes. These equations are fully nonlinear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity solutions. We propose new “direct” discretizations of the nonlocal part of the equation that give rise to monotone schemes capable of handling singular Lévy measures. Furthermore, we develop a new general theory for deriving error estimates for approximate solutions of integro-PDEs, which thereafter is applied to the proposed difference-quadrature schemes.