Extensions
Inequality Constraints
By augmenting the dynamic system with an auxiliary variable, Trimborn (2013) shows how standard algorithms are able to solve the extended dynamic system taking the inequality into account. The procedure can handle any sequence of regimes with binding and non-binding constraints and determines the exact pattern of regimes endogenously.
Solution of continuous-time dynamic models with inequality constraints
Economics Letters, 119, 2013, 299-301
Poisson Shocks
Posch and Trimborn (2013) propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. They transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. They apply the Waveform Relaxation algorithm, i.e., they provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. The authors show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.
Numerical Solution of Dynamic Equilibrium models under Poisson Uncertainty
Journal of Economic Dynamics and Control, 37, 2013, 2602-2622