pfhedge.nn.functional.quadratic_cvar

pfhedge.nn.functional.quadratic_cvar(input, lam, dim=None)

Returns the Quadratic CVaR of the given input tensor.

\[\rho (X) = \inf_\omega \left\{\omega + \lambda || \min\{0, X + \omega\}||_2\right\}.\]

for \(\lambda\geq1\).

References

• Buehler, Hans, Statistical Hedging (March 1, 2019). Available at SSRN: http://dx.doi.org/10.2139/ssrn.2913250 (See Conclusion.)

Parameters

• input (torch.Tensor) – The input tensor.

• lam (float) – The \(lambda\) parameter, representing the weight given to the tail losses.

• dim (int, optional) – The dimension to sort along. If None, the tensor is flattened.

Returns

The Quadratic CVaR of the input tensor.

Return type

torch.Tensor

Examples

>>> from pfhedge.nn.functional import quadratic_cvar
>>>
>>> input = -torch.arange(10.0)
>>> input
tensor([-0., -1., -2., -3., -4., -5., -6., -7., -8., -9.])
>>> quadratic_cvar(input, 2.0)
tensor(7.9750)