Uses a relatively standard MDP algorithm with discrete states/values with VFI and PFI and modified policy iteration
Stationary distribution of the solution
Simulations after solution calculated.
Most are probably available in external libraries for MDPs with a full model. Algorithms are simple but tricky to get high-performance without inplace operations/etc.
https://julia.quantecon.org/dynamic_programming/discrete_dp.html and also https://julia.quantecon.org/multi_agent_models/aiyagari.html also uses it