A model begins with the definition of an event tree, that is a set of nodes linked by probabilities of transitions, without going back.

from bttt import DeterministicTree
tree = DeterministicTree(10) # 10 periods

We set the exogenous values at each node of the tree:

for n in tree.nodes:
    tree.values[n] = 0.1

A model, on a tree can be defined a yaml file. For instance example.yaml contains a section:

equations:
  - -z[s] + etree.values[s]                                         | z[s]
  - -e[s] + a/(a+c)*E[ e[x]   | x in S(s)] + 1.0/(a+c)*(z[s]-f[s])  | e[s]
  - len(s)==1:
    - -Gamma[s] + (e[s]-estar)                                      | Gamma[s]
  - len(s)>1:
    - -Gamma[s] + a/(a+c)*Gamma[P(s)] + beta**t*(e[s]-estar)        | Gamma[s]
  - len(s)==1:
    - -Gamma[s] + E[ Gamma[x] | x in S(s) ] + psi[s] - phi[s]       | f[s]
  - 1<len(s)<len(etree):
    - -Gamma[s] + E[ Gamma[x] | x in S(s) ] + psi[s] - phi[s]       | f[s]
  - len(s)==len(etree):
    - -f[s]                                                         | f[s]
  - -psi[s] + 1000*( Sum[f[x] | x in H(s)] - Rbar  )                | 0 <= psi[s]
  - -phi[s] + (-(f[s]-min_f))*1000                                  | 0 <= phi[s]

By convention, when z is a variable, z[s] denotes the value of z at a node s of the event tree. Equations can be applied to a subset of the nodes, by preceding the equation by a condition, for instance 1<len(s)<len(etree). Complementarity conditions can optionnally be associated to equations. Remark the following elements of syntax:

• P(s) denotes the predecessor of node s
• H(s) denotes the set of all ancestors of node s
• S(s) denotes the set of all successors of node s with the probabilities of transitions.
• Sum[expr[x] | x in H(s)] computes the sum of the expr[x] where x exhausts the set of all ancestors of s.
• E[ Gamma[x] | x in S(s) ] is the expectation of Gamma[s] over all successors of s

The calibration of the model is provided in another section:

calibration:
    beta: 0.8421052631578947
    a: 0.8
    c: 0.15
    estar: -0.0
    Rbar: 1.0
    min_f: 0
    kappa: 1.0
    N: 40
    zbar: 0.1
    p: 1

It is then possible to import and solve the model with:

model = import_tree_model('example.yaml', tree=dt)
sol = model.solve()

The result sol is a mapping associating all variables at all nodes with a value. It can be used to compute simulations.

sim = get_ts(tree, sol, 'e')
print(sim)