Time iteration¶
We consider an fg model, that is a model with the form:
\(s_t = g\left(s_{t1}, x_{t1}, \epsilon_t \right)\)
\(0 = E_t \left[ f\left(s_{t}, x_{t}, s_{t+1}, x_{t+1} \right) \right]\)
where \(g\) is the state transition function, and \(f\) is the arbitrage equation.
The time iteration algorithm consists in approximating the optimal controls, \(x_t = x(s_t)\).
 At step \(n\), the current guess for the control, \(x(s_t) = \varphi^n(s_t)\), serves as the control being exercised next period :
 Given current guess, find the current period’s control by solving the arbitrage equation : \(0 = E_t \left[ f\left(s_{t}, \varphi^{n+1}(s_t), g(s_t, \varphi^{n+1}(s_t)), \varphi^{n}(g(s_t, \varphi^{n+1}(s_t))) \right) \right]\)

dolo.algos.time_iteration.
time_iteration
(model, initial_guess=None, with_complementarities=True, verbose=True, grid={}, maxit=1000, inner_maxit=10, tol=1e06, hook=None)¶ Finds a global solution for
model
using backward timeiteration.This algorithm iterates on the residuals of the arbitrage equations
Parameters: model : NumericModel
“dtmscc” model to be solved
verbose : boolean
if True, display iterations
initial_dr : decision rule
initial guess for the decision rule
with_complementarities : boolean (True)
if False, complementarity conditions are ignored
grid: grid options
maxit: maximum number of iterations
inner_maxit: maximum number of iteration for inner solver
tol: tolerance criterium for successive approximations
Returns: decision rule :
approximated solution

dolo.algos.time_iteration.
residuals_simple
(f, g, s, x, dr, dprocess, parms)¶