def portfolios_to_deterministic(model,pf_names):
#######
#######
import re
regex = re.compile('.*<=(.*)<=.*')
for i,eq in enumerate(model.equations_groups['arbitrage']):
from trash.dolo.symbolic.symbolic import Variable, Equation
m = regex.match(eq.tags['complementarity'])
vs = m.group(1).strip()
if vs in pf_names:
v = Variable(vs)
neq = Equation(v,0)
neq.tag(**eq.tags)
model.equations_groups['arbitrage'][i] = neq
print('Warning : initial model changed')
model.update()
return model
def solve_portfolio_model(model, pf_names, order=2, lambda_name='lam', guess=None):
from dolo.compiler.compiler_python import GModel
if isinstance(model, GModel):
model = model.model
pf_model = model
from dolo import Variable, Parameter, Equation
import re
n_states = len(pf_model.symbols_s['states'])
states = pf_model.symbols_s['states']
steady_states = [Parameter(v.name+'_bar') for v in pf_model.symbols_s['states']]
n_pfs = len(pf_names)
pf_vars = [Variable(v) for v in pf_names]
res_vars = [Variable('res_'+str(i)) for i in range(n_pfs)]
pf_parms = [Parameter('K_'+str(i)) for i in range(n_pfs)]
pf_dparms = [[Parameter('K_'+str(i)+'_'+str(j)) for j in range(n_states)] for i in range(n_pfs)]
from sympy import Matrix
# creation of the new model
import copy
new_model = copy.copy(pf_model)
new_model.symbols_s['controls'] += res_vars
for v in res_vars + pf_vars:
new_model.calibration_s[v] = 0
new_model.symbols_s['parameters'].extend(steady_states)
for p in pf_parms + Matrix(pf_dparms)[:]:
new_model.symbols_s['parameters'].append(p)
new_model.calibration_s[p] = 0
compregex = re.compile('(.*)<=(.*)<=(.*)')
to_be_added_1 = []
to_be_added_2 = []
expressions = Matrix(pf_parms) + Matrix(pf_dparms)*( Matrix(states) - Matrix(steady_states))
for n,eq in enumerate(new_model.equations_groups['arbitrage']):
if 'complementarity' in eq.tags:
tg = eq.tags['complementarity']
[lhs,mhs,rhs] = compregex.match(tg).groups()
mhs = new_model.eval_string(mhs)
else:
mhs = None
if mhs in pf_vars:
i = pf_vars.index(mhs)
neq = Equation(mhs, expressions[i])
neq.tag(**eq.tags)
eq_res = Equation(eq.gap, res_vars[i])
eq_res.tag(eq_type='arbitrage')
to_be_added_2.append(eq_res)
new_model.equations_groups['arbitrage'][n] = neq
to_be_added_1.append(neq)
# new_model.equations_groups['arbitrage'].extend(to_be_added_1)
new_model.equations_groups['arbitrage'].extend(to_be_added_2)
new_model.update()
print("number of equations {}".format(len(new_model.equations)))
print("number of arbitrage equations {}".format( len(new_model.equations_groups['arbitrage'])) )
print('parameters_ordering')
print("number of parameters {}".format(new_model.symbols['parameters']))
print("number of parameters {}".format(new_model.parameters))
# now, we need to solve for the optimal portfolio coefficients
from trash.dolo.numeric.perturbations_to_states import approximate_controls
dr = approximate_controls(new_model)
print('ok')
import numpy
n_controls = len(model.symbols_s['controls'])
def constant_residuals(x, return_dr=False):
d = {}
for i in range(n_pfs):
p = pf_parms[i]
v = pf_vars[i]
d[p] = x[i]
d[v] = x[i]
new_model.set_calibration(d)
# new_model.parameters_values[p] = x[i]
# new_model.init_values[v] = x[i]
if return_dr:
dr = approximate_controls(new_model, order=1, return_dr=True, lambda_name='lam')
return dr
X_bar, X_s, X_ss = approximate_controls(new_model, order=2, return_dr=False, lambda_name="lam")
return X_bar[n_controls-n_pfs:n_controls]
if guess is not None:
x0 = numpy.array(guess)
else:
x0 = numpy.zeros(n_pfs)
print('Zero order portfolios')
print('Initial guess: {}'.format(x0))
print('Initial error: {}'.format( constant_residuals(x0) ))
portfolios_0 = solver(constant_residuals, x0)
print('Solution: {}'.format(portfolios_0))
print('Final error: {}'.format( constant_residuals(portfolios_0) ))
if order == 1:
dr = constant_residuals(portfolios_0, return_dr=True)
return dr
def dynamic_residuals(X, return_dr=False):
x = X[:,0]
dx = X[:,1:]
d = {}
for i in range(n_pfs):
p = pf_parms[i]
v = pf_vars[i]
d[p] = x[i]
d[v] = x[i]
for j in range(n_states):
d[pf_dparms[i][j]] = dx[i,j]
new_model.set_calibration(d)
if return_dr:
dr = approximate_controls(new_model, order=2, lambda_name='lam')
return dr
else:
[X_bar, X_s, X_ss, X_sss] = approximate_controls(new_model, order=3, return_dr=False, lambda_name='lam')
crit = numpy.column_stack([
X_bar[n_controls-n_pfs:n_controls],
X_s[n_controls-n_pfs:n_controls,:],
])
return crit
y0 = numpy.column_stack([x0, numpy.zeros((n_pfs, n_states))])
print('Initial error:')
err = (dynamic_residuals(y0))
print( abs(err).max() )
portfolios_1 = solver(dynamic_residuals, y0)
print('First order portfolios : ')
print(portfolios_1)
print('Final error:')
print(dynamic_residuals(portfolios_1))
dr = dynamic_residuals(portfolios_1, return_dr=True)
# TODO: remove coefficients of criteria
return dr
