4 Quadrants of Dynamic Optimization

1: Discrete-time/deterministic solution using SolveDSGE.jl (@RJDennis). Code link. The corresponding simulations (using 6 different methods):

2: Discrete-time/deterministic solution using POMDPs.jl (@zsunberg) -Code link. See discussion here.

3: Discrete-time/deterministic solution using JuMP.jl (@odow & co) -Please post the code below.

4: Discrete Time/Stochastic, Difference Equations SolveDSGE.jl (@RJDennis) -Code link. The corresponding simulations (using perturbation methods):

5: Discrete Time/Stochastic, Bellman Equations POMDPs.jl (@zsunberg)To Do. -Please post code below using e.g. a 2-state Markov Chain for z.

6: Continuous Time/Deterministic, Bellman Equations (my HJB Solver, based on Ben Moll) -Code link. The corresponding simulations:

7: Continuous Time/Deterministic, Bellman Equations EconPDEs.jl (@matthieu) To Do...

8: Continuous Time/Deterministic, Hamiltonian InfiniteOpt.jl (@pulsipher) -To Do. Only finite horizon currently.

9: Continuous Time/Deterministic, DE SciML.jl (@ChrisRackauckas). -TO DO. Only finite horizon currently. If someone knows how to transform the problem to solve an infinite horizon system please post code below.

10: Continuous Time/Stochastic, Bellman Equations @matthieu (Custom HJB Solver & EconPDEs.jl). To Do.

To Do: Deep learning methods https://discourse.julialang.org/t/solving-hjb-pde-using-deep-learning/60639/13

Transform finite horizon DE, into infinite Horizon DE: https://discourse.julialang.org/t/solving-boundary-value-differential-equation-problems-for-economics/72871