risksim

Portfolio-level loss simulation and aggregate reinsurance modeling.

Overview

risksim composes one or more stochastic loss models into a portfolio, simulates the portfolio's aggregate loss, applies aggregate reinsurance structures, and summarizes the gross, ceded, and retained results. It is intentionally model-agnostic: anything that exposes a .sample(size) method can be a portfolio component, so risksim handles composition, contracts, and simulation summaries while the loss generation lives wherever you like.

It pairs naturally with lossmodels — build a collective-risk model (or any severity/frequency-based model) there, drop it into a risksim portfolio here — but it has no hard dependency on it; its only runtime requirement is numpy.

Highlights

• Portfolios — combine multiple simulated loss components, each with an optional weight, into a single portfolio.
• Aggregate reinsurance — aggregate annual layers (attachment, limit, share) and multi-layer contract programs.
• One simulation, every view — a single run yields gross, ceded, retained, per-component, and per-layer losses.
• Risk measures — mean, variance / standard deviation, VaR, TVaR, exceedance probabilities, and a one-call summary, on any loss vector.
• Model-agnostic — any object implementing .sample(size) works; components that also expose .mean() unlock closed-form portfolio moments.

Installation

pip install risksim

From source:

pip install -e .

Requires Python >=3.10; the only runtime dependency is numpy. The examples below use lossmodels for the component models — install it too if you want to run them as written.

Package structure

risksim/
├── portfolio.py    # Portfolio and PortfolioItem
├── contracts.py    # AggregateLayer, ContractProgram, apply_contract
├── results.py      # SimulationResult (gross / ceded / retained / component / layer views)
├── metrics.py      # mean, variance, std, var, tvar, prob_exceeding, summary
└── protocols.py    # SupportsSample, SupportsMoments

Quick start

from lossmodels import Poisson, Lognormal, CollectiveRiskModel
from risksim import Portfolio, PortfolioItem, AggregateLayer

# two lines of business, each a collective-risk model (any .sample object works)
line_a = CollectiveRiskModel(Poisson(3.0), Lognormal(8.0, 0.9))
line_b = CollectiveRiskModel(Poisson(1.5), Lognormal(9.0, 0.7))

portfolio = Portfolio([
    PortfolioItem("line_a", line_a),
    PortfolioItem("line_b", line_b, weight=1.25),   # optional exposure weight
])

# simulate the portfolio's aggregate annual loss, net of an aggregate layer
layer = AggregateLayer(attachment=250_000, limit=500_000, share=1.0)
result = portfolio.simulate(100_000, contract=layer)

print("gross mean   :", result.gross_mean)
print("ceded mean   :", result.ceded_mean)
print("retained mean:", result.retained_mean)
print("retained 99% VaR :", result.var(0.99))
print(result.summary())

Portfolios

A PortfolioItem wraps a sampleable loss model with a name and an optional weight (a multiplier applied to that component's sampled losses). A Portfolio is a sequence of items.

from risksim import Portfolio, PortfolioItem

port = Portfolio([PortfolioItem("a", model_a), PortfolioItem("b", model_b, weight=0.5)])

gross = port.sample(50_000)              # total portfolio loss per simulation
by_component = port.sample_components(50_000)  # per-component loss matrix
print(port.component_names())

When every component also exposes .mean() / .variance() (the SupportsMoments protocol — which lossmodels models satisfy), the portfolio reports closed-form moments without simulating:

port.mean()       # sum of component means (times weights)
port.std()
port.variance()

simulate(size, contract=None) runs the portfolio and returns a SimulationResult; sample(size) returns just the gross loss vector.

Aggregate reinsurance

An AggregateLayer is an aggregate annual structure defined by three numbers:

• attachment — the aggregate retention; losses below it are not ceded.
• limit — the width of the layer above the attachment (None = unlimited).
• share — the ceded proportion of the layer (e.g. 0.8 for an 80% placement).

For a gross annual loss L, the ceded amount is share × min(max(L − attachment, 0), limit).

from risksim import AggregateLayer, ContractProgram, apply_contract

# a single layer: 80% of the 500k aggregate layer above a 250k retention
layer = AggregateLayer(attachment=250_000, limit=500_000, share=0.8)

# stack layers into a program (e.g. a working layer plus a higher layer)
program = ContractProgram([
    AggregateLayer(attachment=250_000, limit=500_000, share=1.0, name="working"),
    AggregateLayer(attachment=750_000, limit=1_000_000, share=0.5, name="higher"),
])

# apply either to a loss vector directly
ceded, retained = apply_contract(gross_losses, program)

apply_contract(losses, contract) returns (ceded, retained) arrays aligned with the input, where ceded + retained == losses. Passing a contract to Portfolio.simulate(..., contract=program) does the same inside the simulation and records the per-layer detail.

The simulation result

SimulationResult holds every view from a single run and computes risk measures on demand:

Risk measures

The metrics module operates on any loss vector (a NumPy array or list), so you can use it independently of the portfolio machinery:

from risksim import metrics

metrics.mean(losses)
metrics.std(losses)            # metrics.variance(...) also available
metrics.var(losses, 0.99)      # 99% VaR
metrics.tvar(losses, 0.99)     # 99% TVaR
metrics.prob_exceeding(losses, 1_000_000)
metrics.summary(losses, quantiles=(0.95, 0.99, 0.995))

The SupportsSample protocol

Any object implementing sample(size: int) -> np.ndarray can be a portfolio component — a lossmodels collective-risk model or severity, a custom class, or a thin wrapper around a sampler. Components that additionally implement mean() / variance() (SupportsMoments) enable the closed-form Portfolio.mean() / .std() / .variance() shortcuts.

The OpenActuarial ecosystem

risksim is the portfolio-and-reinsurance layer of a small family of actuarial packages that interoperate through the .sample() / .mean() interface:

• lossmodels — frequency / severity distributions, aggregate (collective-risk) loss models, coverage modifications, and model fitting. The natural source of risksim portfolio components.
• extremeloss — extreme value theory for tail fitting and tail risk measures. It can analyze a risksim simulation directly (e.g. losses_from_risksim(...) and tail_summary_from_risksim(...)).
• actuarialpy — deterministic, experience-and-data analysis (summaries, triangles, trend, credibility) on tabular data.

Testing

pytest -q

License

MIT License