lr_values = [0.001, 0.0001, 0.00001]
xi = tf.random_uniform((batch_size, d), minval=90., maxval=110., dtype=dtype)
def phi(x, axis=1):
return np.exp(-r * T) \
* tf.maximum(K - tf.reduce_min(x, axis=axis, keepdims=True), 0.)
def mc_body(idx, p):
_w = tf.matmul(
tf.random_normal((mc_samples_ref * batch_size, d),
stddev=np.sqrt(T / N),
dtype=dtype), sigma)
_w = tf.reshape(_w, (mc_samples_ref, batch_size, d))
_x = xi * tf.exp((r - c - 0.5 * (beta * sigma_norms)**2) * T + beta * _w)
return idx + 1, p + tf.reduce_mean(phi(_x, 2), axis=0)
x_sde = xi * tf.exp(
(r - c - 0.5 * (beta * sigma_norms)**2) * T + beta * tf.matmul(
tf.random_normal(
(batch_size, d), stddev=np.sqrt(T / N), dtype=dtype), sigma))
_, u = tf.while_loop(lambda idx, p: idx < mc_rounds_ref, mc_body,
(tf.constant(0), tf.zeros((batch_size, 1), dtype)))
u_reference = u / tf.cast(mc_rounds_ref, tf.float32)
kolmogorov_train_and_test(xi, x_sde, phi, u_reference, neurons, lr_boundaries,
lr_values, train_steps, mc_rounds, mc_freq,
'example_bs_model_with_correlated_noise.csv', dtype)
neurons = [d + 100, d + 100, 1]
train_steps = 750000
mc_rounds, mc_freq = 10, 25000
mc_samples_ref, mc_rounds_ref = 1024, 1024
lr_boundaries = [250001, 500001]
lr_values = [0.001, 0.0001, 0.00001]
xi = tf.random_uniform(shape=(batch_size, d),
minval=90.,
maxval=110.,
dtype=dtype)
def phi(x, axis=1):
return np.exp(-r * T) * tf.maximum(
tf.reduce_max(x, axis=axis, keep_dims=True) - K, 0.)
def mc_body(idx, p):
_x = xi * tf.exp((r - c - 0.5 * sigma**2) * T + sigma * tf.random_normal(
(mc_samples_ref, batch_size, d), stddev=np.sqrt(T / N), dtype=dtype))
return idx + 1, p + tf.reduce_mean(phi(_x, 2), axis=0)
x_sde = xi * tf.exp((r - c - 0.5 * sigma**2) * T + sigma * tf.random_normal(
(mc_samples_ref, batch_size, d), stddev=np.sqrt(T / N), dtype=dtype))
_, u = tf.while_loop(lambda idx, p: idx < mc_rounds_ref, mc_body,
(tf.constant(0), tf.zeros((batch_size, 1), dtype)))
u_reference = u / tf.cast(mc_rounds_ref, tf.float32)
kolmogorov_train_and_test(xi, x_sde, phi, u_reference, neurons, lr_boundaries,
lr_values, train_steps, mc_rounds, mc_freq,
'example3_3.csv', dtype)
mc_samples_ref, mc_rounds_ref = 1024, 1024
lr_boundaries = [250001, 500001]
lr_values = [0.001, 0.0001, 0.00001]
xi = tf.random_uniform((batch_size, d), minval=90., maxval=110., dtype=dtype)
def phi(x, axis=1):
return np.exp(-r * T) \
* tf.maximum(tf.reduce_max(x, axis=axis, keepdims=True) - K, 0.)
def mc_body(idx, p):
_x = xi * tf.exp((r - c - 0.5 * sigma ** 2) * T + sigma
* tf.random_normal((mc_samples_ref, batch_size, d),
stddev=np.sqrt(T / N), dtype=dtype))
return idx + 1, p + tf.reduce_mean(phi(_x, 2), axis=0)
x_sde = xi * tf.exp((r - c - 0.5 * sigma ** 2) * T
+ sigma * tf.random_normal((batch_size, d),
stddev=np.sqrt(T / N),
dtype=dtype))
_, u = tf.while_loop(lambda idx, p: idx < mc_rounds_ref, mc_body,
(tf.constant(0), tf.zeros((batch_size, 1), dtype)))
u_reference = u / tf.cast(mc_rounds_ref, tf.float32)
kolmogorov_train_and_test(xi, x_sde, phi, u_reference, neurons,
lr_boundaries, lr_values, train_steps,
mc_rounds, mc_freq, 'example_geometric_brownian_motions.csv', dtype)
_sqrt_v)
+ sigma / 2. * dw_2) ** 2
+ (kappa * theta - sigma ** 2 / 4. - kappa * v) * h, 0.)
def mc_body(idx, p):
_, _x, __v = tf.while_loop(
lambda _idx, s, v: _idx < N,
lambda _idx, s, v: sde_body(_idx, s, v, mc_samples_ref), loop_var_mc)
return idx + 1, p + tf.reduce_mean(phi(_x, 2), axis=0)
loop_var_mc = (tf.constant(0),
tf.ones(
(mc_samples_ref, batch_size, d / 2), dtype) * tf.log(S_0),
tf.ones((mc_samples_ref, batch_size, d / 2), dtype) * V_0)
loop_var = (tf.constant(0), tf.ones(
(1, batch_size, d / 2), dtype) * tf.log(S_0),
tf.ones((1, batch_size, d / 2), dtype) * V_0)
_, x_sde, _v = tf.while_loop(lambda idx, s, v: idx < N,
lambda idx, s, v: sde_body(idx, s, v, 1),
loop_var)
_, u = tf.while_loop(lambda idx, p: idx < mc_rounds_ref, mc_body,
(tf.constant(0), tf.zeros((batch_size, 1), dtype)))
u_reference = u / tf.cast(mc_rounds_ref, tf.float32)
kolmogorov_train_and_test(xi, tf.squeeze(x_sde,
axis=0), phi, u_reference, neurons,
lr_boundaries, lr_values, train_steps, mc_rounds,
mc_freq, 'example_heston_model.csv', dtype)
def sde_body(idx, s, samples):
return tf.add(idx, 1), s \
+ tf.cast(T / N * tf.sqrt(phi(mu(s), 2 if samples > 1 else 1))
<= 1., dtype) * mu(s) * T / N \
+ beta * tf.random_normal((samples, batch_size, d),
stddev=np.sqrt(T / N), dtype=dtype)
def mc_body(idx, p):
_, _x = tf.while_loop(lambda _idx, s: _idx < N,
lambda _idx, s: sde_body(_idx, s, mc_samples_ref),
loop_var_mc)
return idx + 1, p + tf.reduce_mean(phi(_x, 2), axis=0)
loop_var_mc = (tf.constant(0), tf.ones(
(mc_samples_ref, batch_size, d), dtype) * xi)
loop_var = (tf.constant(0), tf.ones((1, batch_size, d), dtype) * xi)
_, x_sde = tf.while_loop(lambda idx, s: idx < N,
lambda idx, s: sde_body(idx, s, 1), loop_var)
_, u = tf.while_loop(lambda idx, p: idx < mc_rounds_ref, mc_body,
(tf.constant(0), tf.zeros((batch_size, 1), dtype)))
u_reference = u / tf.cast(mc_rounds_ref, tf.float32)
kolmogorov_train_and_test(xi, tf.squeeze(x_sde, axis=0), phi, u_reference,
neurons, lr_boundaries, lr_values, train_steps,
mc_rounds, mc_freq,
'example_stochastic_lorenz_equation.csv', dtype)