optimal_stopping

Variations on Solutions to Optimal Stopping Problems

See Ben Moll's Heterogeneous Agent Models in Continuous Time project. In particular

• Stopping Time Problem I: Exercising an Option:: with http://www.princeton.edu/~moll/HACTproject/option_simple_LCP.m
• Stopping Time Problem II: Liquid and Illiquid Assets and Fixed Adjustment Costs:: with http://www.princeton.edu/~moll/HACTproject/liquid_illiquid_LCP.m

Simple Example with a Diffusion

While the application here is for a stopping problem with a diffusion, many of the examples here are simply about the discretizaiton step for the HJBE.

• The file simple_optimal_stopping_diffusion.m is a annotated variation on http://www.princeton.edu/~moll/HACTproject/option_simple_LCP.m which uses same linear-complementarity problem solver LCP.m as the HACTproject
• The file simple_optimal_stopping_diffusion_tomlab.m is a variation which uses tomlab's linear complementarity solver instead. While Tomlab's algorithms are overkill for this simple problem, they may become required for more complicated setups with more dimensions or nonlinearity.
• simple_optimal_stopping_diffusion_nonlinear_tomlab.m: sets up the problem as a (potentially) nonlinear complementarity problem. While this exactly is clearly linear, a control markov process for the diffusion would lead to nonlinearities, and this serves as a test bed for how to write those types of problems.
• simple_optimal_stopping_diffusion_non_uniform_grid_tomlab.m: variation with a non-uniform grid. Important for cases where the nonlinearity occur in known areas of the state space.