Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Penalty methods for American options with stochastic volatility
Journal of Computational and Applied Mathematics
The efficient solution of linear complementarity problems for tridiagonal Minkowski matrices
ACM Transactions on Mathematical Software (TOMS)
Quadratic Convergence for Valuing American Options Using a Penalty Method
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A penalty method for American options with jump diffusion processes
Numerische Mathematik
Accurate Evaluation of European and American Options Under the CGMY Process
SIAM Journal on Scientific Computing
Valuation of Stock Loans with Regime Switching
SIAM Journal on Control and Optimization
American Options in Regime-Switching Models
SIAM Journal on Control and Optimization
Some Convergence Results for Howard's Algorithm
SIAM Journal on Numerical Analysis
Optimal Switching over Multiple Regimes
SIAM Journal on Control and Optimization
Option pricing with regime switching by trinomial tree method
Journal of Computational and Applied Mathematics
A Numerical Analysis of American Options with Regime Switching
Journal of Scientific Computing
Is Regime Switching in Stock Returns Important in Portfolio Decisions?
Management Science
An iterative method for pricing American options under jump-diffusion models
Applied Numerical Mathematics
A Finite Time Horizon Optimal Stopping Problem with Regime Switching
SIAM Journal on Control and Optimization
Trend Following Trading under a Regime Switching Model
SIAM Journal on Financial Mathematics
Penalty Methods for the Solution of Discrete HJB Equations—Continuous Control and Obstacle Problems
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
Journal of Scientific Computing
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We analyze a number of techniques for pricing American options under a regime switching stochastic process. The techniques analyzed include both explicit and implicit discretizations with the focus being on methods which are unconditionally stable. In the case of implicit methods we also compare a number of iterative procedures for solving the associated nonlinear algebraic equations. Numerical tests indicate that a fixed point policy iteration, coupled with a direct control formulation, is a reliable general purpose method. Finally, we remark that we formulate the American problem as an abstract optimal control problem; hence our results are applicable to more general problems as well.