Weekly exercise 14: Stochastic consumption-savings model in finite horizon¶

In this exercise you continue building up the deaton() class by adding the finite horizon version of the model.

Start by copying the deaton() class code from lecture notebook 36. Make the following modifications:

add an attribute horizon to the model which is set to ‘infinite’ by default, but can take numerical values fixing the number of periods in the model $ T $
modify the __repr__() method to output whether the model is finite or infinite horizon
code up the backwards induction solver for the finite horizon version of the model in a separate method solver_backwards_induction() with the only argument callback function (but using horizon attribute for the maximum number of periods). See lecture notebook 27 for examples of backward induction solvers
modify the simulator method to default to the $ T $ set in the horizon attribute when it is not equal ‘infinite’

Run separate simulations of the model for a few values of parameters, and discuss their similarities and differences.

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# Your code here

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m = deaton(ngrid=100,nchgrid=250,sigma=.2,R=1.05,beta=.975,nquad=10)
m.horizon=12
print(m)
v,c = m.solve_plot(solver='vfi')
sims = m.simulator(init_wealth=[1,2,3],T=5)