pricing.RiskProfile

A risk profile for property per-risk business: bands of sum insured,

Usage

pricing.RiskProfile()

each with an expected loss (given, or premium times a loss ratio) and its own exposure curve.

Each band’s representative risk has sum insured SI (its total sum insured over its number of risks, say), taken as its MPL. The band expects EL / (SI * curve.mean_rate) losses a year; each simulated loss is the band’s SI times a destruction rate from the band’s curve, and carries that SI, so a surplus treaty (Layer.surplus) and the per-risk excess of loss it inures to apply to the events. The exposure-rated expectations (expected_layer_loss, expected_surplus_loss) check the simulation.

Parameters

sums_insured: list of float: One per band.
risks: list of float: Number of risks per band (for reference).
curves: Mbbefd or TabulatedCurve, or a list of them: One curve for every band, or one per band.
expected_losses: list of float: Expected annual loss per band. Give this, or premiums.
premiums: list of float: Premium per band, with loss_ratio.
loss_ratio: float or list of float: Expected loss ratio, one for all bands or one per band.
lower: list of float or None: Bounds of each band’s sums insured (None for a band without). A band with bounds spreads its risks’ sums insured uniformly between them: its mean SI is (lower + upper) / 2 (in place of sums_insured), each simulated loss draws its own SI between the bounds, and the exposure-rated expectations average over the band, weighted by sum insured.
upper: list of float or None: Bounds of each band’s sums insured (None for a band without). A band with bounds spreads its risks’ sums insured uniformly between them: its mean SI is (lower + upper) / 2 (in place of sums_insured), each simulated loss draws its own SI between the bounds, and the exposure-rated expectations average over the band, weighted by sum insured.
spread: (uniform, tilted) = "uniform": How a band with bounds spreads its sums insured. "tilted" keeps sums_insured as the mean, so the spread matches both the bounds and the band’s total sum insured: the density ∝ exp(θ s) on the bounds with θ solved for that mean (sums_insured must lie strictly between the bounds).

Examples

>>> from prospicio.pricing import Mbbefd, RiskProfile
>>> p = RiskProfile([1e6, 10e6], [800, 50], Mbbefd.swiss_re(3.0),
...                 premiums=[2e6, 1e6], loss_ratio=0.6)
>>> round(p.expected_loss())

1800000

>>> events = p.simulate(1000, 7)
>>> events.has_sums_insured

True

Methods

Name	Description
expected_claims()	Expected number of losses a year, per band.
expected_layer_loss()	Exposure-rated expected loss to a per-risk layer limit xs
expected_loss()	Expected annual loss, all bands.
expected_surplus_loss()	Expected annual loss ceded to a surplus treaty.
simulate()	n_sims years of losses, each with its risk’s sum insured.

expected_claims()

Expected number of losses a year, per band.

Usage

expected_claims()

Returns

list of float

expected_layer_loss()

Exposure-rated expected loss to a per-risk layer limit xs

Usage

expected_layer_loss(
    limit, attachment, surplus_retention=None, surplus_lines=None
)

attachment, optionally on each risk net of a surplus treaty.

Parameters

limit: float: inf for unlimited.
attachment: float
surplus_retention: float = None: A surplus treaty the layer inures to.
surplus_lines: float = None: A surplus treaty the layer inures to.

Returns

float

expected_loss()

Expected annual loss, all bands.

Usage

expected_loss()

Returns

float

expected_surplus_loss()

Expected annual loss ceded to a surplus treaty.

Usage

expected_surplus_loss(retention, lines)

Parameters

retention: float
lines: float

Returns

float

simulate()

n_sims years of losses, each with its risk’s sum insured.

Usage

simulate(n_sims, seed)

Parameters

n_sims: int
seed: int

Returns

EventSet