risk.esscher_allocation()

Esscher allocation: each component’s mean under the Esscher transform

Usage

risk.esscher_allocation(
    pd,
    h,
)

of the total, E[X_j exp(h S)] / E[exp(h S)].

The contributions sum to esscher(pd, h); at h = 0 they are the means.

Parameters

pd: PredictiveDistribution

h: float

Returns

list of float

One per component, in pd.components() order.

Examples

>>> from prospicio.distributions import PredictiveDistribution
>>> from prospicio.risk import esscher_allocation
>>> pd = PredictiveDistribution(["lob"], [("motor",), ("property",)],
...                             [[1.0, 2.0], [4.0, 1.0], [2.0, 5.0], [3.0, 6.0]])
>>> esscher_allocation(pd, 0.0)

[2.5, 3.5]