Newton's method for B-differentiable equations
Mathematics of Operations Research
Numerical methods for stochastic control problems in continuous time
SIAM Journal on Control and Optimization
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Quadratic Convergence for Valuing American Options Using a Penalty Method
SIAM Journal on Scientific Computing
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Tools for Computational Finance (Universitext)
Tools for Computational Finance (Universitext)
Automatica (Journal of IFAC)
A Semi-Lagrangian Approach for Natural Gas Storage Valuation and Optimal Operation
SIAM Journal on Scientific Computing
Maximal Use of Central Differencing for Hamilton-Jacobi-Bellman PDEs in Finance
SIAM Journal on Numerical Analysis
Some Convergence Results for Howard's Algorithm
SIAM Journal on Numerical Analysis
Continuous-time Stochastic Control and Optimization with Financial Applications
Continuous-time Stochastic Control and Optimization with Financial Applications
A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance
SIAM Journal on Numerical Analysis
Methods for Pricing American Options under Regime Switching
SIAM Journal on Scientific Computing
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In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalization error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent iterative solvers for the penalized equations. Furthermore, we discuss under what conditions local quadratic convergence of the iterative solvers can be expected. We include numerical results demonstrating the competitiveness of our methods.