"w" in def CVaR()

[NikolausKCL]

What is the input "w" in the CVaR loss function.

def CVaR(wealth = None, w = None, loss_param = None):
    alpha = loss_param
    # Expected shortfall risk measure
    return K.mean(w + (K.maximum(-wealth-w,0)/(1.0-alpha)))

How do I have to initialize it in order to avoid the following error:

optimizer = Adam(learning_rate=lr)

# Setup and compile the model
model_simple = Deep_Hedging_Model(N=N, d=d+2, m=m, risk_free=risk_free, \
          dt = dt, strategy_type="simple", epsilon = epsilon, \
          use_batch_norm = use_batch_norm, kernel_initializer = kernel_initializer, \
          activation_dense = activation_dense, activation_output = activation_output, \
          final_period_cost = final_period_cost, delta_constraint = delta_constraint, \
          share_stretegy_across_time = share_stretegy_across_time, \
          cost_structure = cost_structure)
loss = CVaR(model_simple.output,None,loss_param)
model_simple.add_loss(loss)

model_simple.compile(optimizer=optimizer)

early_stopping = EarlyStopping(monitor="loss", \
          patience=10, min_delta=1e-4, restore_best_weights=True)
reduce_lr = ReduceLROnPlateau(monitor="loss", \
          factor=0.5, patience=2, min_delta=1e-3, verbose=0)

callbacks = [early_stopping, reduce_lr]

# Fit the model.
model_simple.fit(x=xtrain, batch_size=batch_size, epochs=epochs, \
          validation_split=0.1, verbose=1)

#clear_output()

print("Finished running deep hedging algorithm! (Simple Network)")
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
[<ipython-input-68-f4e901423d20>](https://localhost:8080/#) in <module>()
      3 # Setup and compile the model
      4 model_simple = Deep_Hedging_Model(N=N, d=d+2, m=m, risk_free=risk_free,           dt = dt, strategy_type="simple", epsilon = epsilon,           use_batch_norm = use_batch_norm, kernel_initializer = kernel_initializer,           activation_dense = activation_dense, activation_output = activation_output,           final_period_cost = final_period_cost, delta_constraint = delta_constraint,           share_stretegy_across_time = share_stretegy_across_time,           cost_structure = cost_structure)
----> 5 loss = CVaR(model_simple.output,None,loss_param)
      6 model_simple.add_loss(loss)
      7 

3 frames
[/usr/local/lib/python3.7/dist-packages/keras/utils/traceback_utils.py](https://localhost:8080/#) in error_handler(*args, **kwargs)
     65     except Exception as e:  # pylint: disable=broad-except
     66       filtered_tb = _process_traceback_frames(e.__traceback__)
---> 67       raise e.with_traceback(filtered_tb) from None
     68     finally:
     69       del filtered_tb

ValueError: Exception encountered when calling layer "tf.math.subtract_2" (type TFOpLambda).

Tried to convert 'y' to a tensor and failed. Error: None values not supported.

Call arguments received:
  • x=tf.Tensor(shape=(None, 1), dtype=float32)
  • y=None
  • nam
3 frames
[/usr/local/lib/python3.7/dist-packages/keras/utils/traceback_utils.py](https://localhost:8080/#) in error_handler(*args, **kwargs)
     65     except Exception as e:  # pylint: disable=broad-except
     66       filtered_tb = _process_traceback_frames(e.__traceback__)
---> 67       raise e.with_traceback(filtered_tb) from None
     68     finally:
     69       del filtered_tb

ValueError: Exception encountered when calling layer "tf.math.subtract_2" (type TFOpLambda).

Tried to convert 'y' to a tensor and failed. Error: None values not supported.

Call arguments received:
  • x=tf.Tensor(shape=(None, 1), dtype=float32)
  • y=None
  • name=None
```e=None