Continuous vs. Discrete Time: Some Computational Insights

Solving a workhorse incomplete markets model in continuous time is many times faster compared to its discrete time counterpart. This paper dissects the computational discrepancies and identifies the key bottlenecks. The implicit finite difference method – a commonly used tool in continuous time – accounts for a large share of the difference. This method is shown to be a special case of Howard’s improvement algorithm, efficiently implemented by relying on sparse matrix operations. By representing the policy function with a transition matrix it is possible to formulate a similar procedure in discrete time, which effectively eliminates the differences in run-times entirely.