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Solve_Generic_HJB_KFE

Julia code to solve generic HJBs & KFEs

Current code: deterministic, one state, one control, infinite horizon, time/state separable
Currently, the return function only depends on the control, not the state (as in durable goods etc)
Challenge: for true generality, need to solve non-linear system of n_c focs, to get n_c policy functions (but the number of iterations w/ the implicit scheme is usually small so perhaps it's not too bad???)

Current examples:

  • NGM: 1-state (k), 1-choice (c), return u(c), compare w/ closed form
  • NGM (Convex-Concave tech): 1-state (k), 1-choice (c), return u(c), compare w/ Hamiltonian (multiple SS)
  • CS: 1-state (a), 1-choice (c), return u(c), compare w/ closed form {To Do: extend to finite horizon}
  • Investment: 1-state (k), 1-choice (i), return profit(k,i) {Not working well}
  • Housing:
  • Labor: non-stochastic

Next: human capital/deterministic labor supply/deterministic Lifecycle
Next: combine 2-state Poisson & Diffusion into a generic solver

Extensions:
endog := endogenous & exog := exogenous

Optimal stopping time (HJBVI, LCP)

Q: what about GE models w/ non-constant interest rates & paths of prices?

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Julia code to solve generic HJBs & KFEs

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