def baseline_utility(x, alpha):
""" This function returns the baseline utility.
"""
# Guard interface.
assert basic_checks('baseline_utility', 'in', x, alpha)
# Calculate utility.
rslt = x ** alpha
# Check result.
assert basic_checks('baseline_utility', 'out', rslt)
# Finishing
return rslt
def _wrapper_baseline(alpha, shape, x):
""" This private function constructs the integrand for the application of
numerical integration strategies.
"""
# Guard interface.
assert basic_checks('_wrapper_baseline', 'in', alpha, shape, x)
# Evaluate utility and weigh by probability.
rslt = baseline_utility(x, alpha) * lognorm.pdf(x, shape)
# Check result.
assert basic_checks('_wrapper_baseline', 'out', rslt)
# Finishing
return rslt
def get_baseline_lognormal(alpha, shape, technique, int_options):
""" Get the expected returns by drawing numerous random deviates from a
lognormal distribution.
"""
# Guard interface.
args = (alpha, shape, technique, int_options)
assert basic_checks('get_baseline_lognormal', 'in', args)
# Construct bounds based on quantiles of lognormal distribution.
lower, upper = EPS, lognorm.ppf(0.9999999, shape)
# Prepare wrapper for alternative integration strategies.
func = partial(_wrapper_baseline, alpha, shape)
# Perform native monte carlo integration.
if technique == 'naive_mc':
# Distribute relevant integration options.
implementation = int_options['naive_mc']['implementation']
num_draws = int_options['naive_mc']['num_draws']
seed = int_options['naive_mc']['seed']
# Perform naive Monte Carlo integration.
rslt = naive_monte_carlo(func, (lower, upper), num_draws,
implementation, seed)
elif technique == 'quad':
# Perform integration based on quadrature.
rslt = scipy_quad(func, (lower, upper))
elif technique == 'romberg':
# Perform integration based on Romberg.
rslt = scipy_romberg(func, (lower, upper))
else:
pass
# Check result.
assert basic_checks('get_baseline_lognormal', 'out', rslt)
# Finishing
return rslt