It turns out the firm investment model used in the example above can be solved very precisely in all 4 quadrants using e.g. MatrixEquations.jl.
Hat tip to @baggepinnen & @andreasvarga for their help
Here are infinite horizon versions of all 4 quadrants:
Here is the math to formulate the firm investment problem as LQ/LQG:
I’ll post the code later…
- Above I solve infinite horizon versions in all 4 quadrants.
MatrixEquations.jlcurrently does not solve finite horizon versions (that I could find…)
QuantEcon.jl solves the finite horizon version, only in discrete time (not continuous time)
Would be nice if the Riccatti solvers in both packages were benchmarked/compared… - Symbolics.jl works insanely well (at least for what I needed so far).
Though it took me a lot of time to figure out how to use it. I’m sure the docs will improve…