def optimize(optional_asset, market_assumptions, nb_simulations=1000, regression=polynomial_regression):
discount_factor = market_assumptions.discount_factor
exercise_times = list(optional_asset.exercise_times)
simulation_timeline = sorted(set([0.0] + exercise_times))
# create a simulator, we will go backward
# TODO only simulate required uncertainties.
simulator = BidirectionalSimulator(
market_assumptions.uncertainty_system, simulation_timeline, nb_simulations, antithetic=True
)
simulator.go_end()
bellman_values_shape = (1, simulator.nb_simulations)
next_bellman_values = defaultdict(lambda: np.zeros(bellman_values_shape))
# set terminal values
# conditional_expectancy_store contains for a given t,
# the expected return of the asset at t+, knowing the state of the asset
# at t+
conditional_expectancy_store = ConditionalExpectancyStore()
nb_exercises = len(exercise_times) - 1
t_final = simulation_timeline[-1]
# considering the state accessible at the last exercise date...
for asset_state in optional_asset.get_accessible_states(nb_exercises - 1):
# we check all the accessible state at the next step :
for command in asset_state.get_commands(t_final):
final_state = command.dest_state
conditional_expectancy_store.set(simulator.tid, final_state, final_state.get_final_value(simulator.tid))
bellman_values = np.zeros((1, simulator.nb_simulations))
# backward optimization
for t in exercise_times[::-1]:
discount_factor_t = discount_factor(t)
cur_bellman_values = defaultdict(lambda: defaultdict(lambda: 0.0))
t_id = simulator.tid
# TODO differentiate simulation timeline and asset timeline.
for asset_state in optional_asset.get_accessible_states(t_id):
# returns the bellman values for all simulations
bellman_values_if_commands = compute_expected_value_foreach_command(
asset_state, simulator.state, conditional_expectancy_store, market_assumptions.discount_factor
)
# optimal command
optimal_command_id = compute_optimal_command(
asset_state, simulator.state, conditional_expectancy_store, discount_factor
)
bellman_values = 0.0
commands = asset_state.get_commands(t)
bellman_values_if_command = np.zeros((len(commands), simulator.nb_simulations))
for (command_id, command) in enumerate(commands):
bellman_values_if_command[command_id : command_id + 1, :] = (
command.payoff(simulator.state) * discount_factor_t + next_bellman_values[command.dest_state]
)
bellman_values = bellman_values_if_command[optimal_command_id, np.arange(simulator.nb_simulations)].reshape(
1, simulator.nb_simulations
)
cur_bellman_values[asset_state] = bellman_values
regression_information = asset_state.extract_markov_state(simulator.previous)
conditional_expectancy = compose(
regression(regression_information, bellman_values), optional_asset.extract_markov_state
)
conditional_expectancy_store.set(t_id - 1, asset_state, conditional_expectancy)
next_bellman_values = cur_bellman_values
simulator.go_back()
mtm = MonteCarloEstimation(bellman_values, antithetic=antithetic)
return OptimizedAsset(optional_asset, conditional_expectancy_store, mtm)