Using aggregate

Very short introductions to aggregate by feature

Author

Stephen J. Mildenhall

This site is a series of short introductions to aggregate arranged by feature. Each page explains the purpose of the feature, the mathematics in a line or two, and then gives short worked examples. All the code is shown along with its output. The version of aggregate used is given in the page footer. A page takes only a few minutes to read. Each is also available as a PDF from a link on the page, and all of them combined, in alphabetical order with a table of contents, from the link at the top right. Every page is tagged by topic, such as reinsurance, pricing, or numerics. The tags are listed beside the index with the number of pages for each, and selecting a tag, there or on an entry, shows only the pages with that tag.

You can run any page yourself. The Code menu at the top of a page reveals all the page source. The pages import a few helpers from style.py: wprint prints a long string wrapped at 80 characters, with the system temporary folder shown as <tmp>; GT formats a table; and refuse builds a program that is expected to fail and prints the error. All the DecL programs on these pages also run in the aggregate Loss Lab, in the browser, with no installation.

Using `aad` and `agglimit`

Annual aggregate deductible and aggregate limit on an occurrence layer (aad, agglimit)

reinsurance

Using `AllocationBounds`

Ranges of the natural allocation of a portfolio premium to each unit over all distortions that price the total

bounds

allocation

Using `approximate`

Method-of-moments approximations to an aggregate distribution and their error in the tail

distributions

numerics

Using `bivariate`

Joint distribution of two aggregates sharing one claim count, coupled by a copula or a discrete bivariate severity

bivariate

Using `Bounds`

Pricing bounds: the envelope of all distortions that price a risk to a given premium with given assets

bounds

pricing

Using `AggregateCHF` with stable laws

Accurate stable distributions by tilted inversion, checked against scipy

distributions

numerics

Using `AggregateCHF`

Distributions computed by inverting a characteristic function

distributions

numerics

Using `clash`

Clash covers on two units hit by the same events with the clash statement

bivariate

reinsurance

catastrophe

Using deductibles

Franchise and disappearing deductibles in the DecL layers clause

severity

Using distortions

Distortion functions for risk-adjusted pricing with the DecL distortion statement and the Distortion class

pricing

Using `elt` with files

Event loss tables read from CSV and Parquet files with the elt clause

catastrophe

Using `elt`

Aggregates from event loss tables with the elt clause

catastrophe

Using explanations

The description and explanation strings on aggregate objects

output

Using `grossnet`, `grossceded` and `netceded`

Joint distribution of gross, ceded and net loss under occurrence reinsurance with the view-pair prefixes

bivariate

reinsurance

Using help

Help in aggregate with decl_help, the help method, and parse error reports

output

DecL

Using labels

Display labels on statements, layers, reinsurance, expenses, and premium with the DecL as clause

DecL

output

P&L

Using lattice buckets

Exact bucket sizes for discrete severities on a dyadic lattice

numerics

severity

reinsurance

Using loss corridors

Loss ratio corridors retained by the cedant on an aggregate quota share with the DecL corridor clause

reinsurance

variable feature

P&L

Using `nttagg`

Exact compound distributions with the nttagg kind and the number-theoretic transform

numerics

Using occurrence reinsurance

Per-occurrence excess of loss layers, partial placements and towers (occurrence net of, occurrence ceded to)

reinsurance

Using `oep`

Occurrence exceeding probability and occurrence PML of a Poisson aggregate, compared with aggregate PML (oep)

catastrophe

Using `pollaczeck_khinchine` and `wiener_hopf`

Eventual ruin probability with pollaczeck_khinchine and wiener_hopf

ruin

Using `pnl` and `xpnl`

Profit and loss statements with the pnl and xpnl kinds and the PnL class

P&L

reinsurance

pricing

Using `price` and `evaluate`

Premiums from distortions and breakeven distortions from premiums on an Aggregate with price, price_pentagon and evaluate

pricing

Using `price`

Distorted ask and bid prices of a loss distribution with Distortion.price and Aggregate.price

pricing

Using `PricingBounds`

Exact price ranges of other risks over all distortions that price a reference risk to a given premium

bounds

pricing

Using profit commissions

Profit commissions on an aggregate quota share with the DecL pc clause

reinsurance

variable feature

P&L

Using recipes

The Underwriter recipe base: the library included with aggregate, the reproductions corpus and your own DecL

DecL

Using reinstatements

Paid reinstatements on an occurrence layer, with a ceded premium that varies with the annual recovery

reinsurance

variable feature

P&L

Using renewal counts

Renewal claim counts with a years exposure and the wait and dwait clauses

frequency

Using retro rating

Retrospectively rated premium for a large account, set by the account’s own loss between a minimum and a maximum

variable feature

P&L

pricing

Using `eventual_ruin`

Eventual ruin at a stated margin and capital with Aggregate.eventual_ruin

ruin

Using severity parameters

Shape parameters, scale and location, the mean and CV form, and the _ placeholder in a mixture of severity families

severity

DecL

Using `sharpen`

Auditing the FFT grid with sharpen on Aggregate and Portfolio

numerics

Using sliding scale commissions

Sliding scale ceding commissions on an aggregate quota share with the DecL slide clause

reinsurance

variable feature

P&L

Using `ssev`

Signed severities with ssev, and aggregates or portfolios as severities

severity

Using `stable` names and arithmetic

Named stable and tweedie laws, and arithmetic on stable references

distributions

DecL

Using `stable`

Stable laws with the stable statement and aggregate.stable.Stable

distributions

Using the structure chart

Reinsurance program diagrams of layers, shares and retentions, with optional Lee curves (the structure chart)

reinsurance

charts

Using swing rating

Swing-rated aggregate reinsurance, with a ceded premium set by the ceded loss between a minimum and a maximum

reinsurance

variable feature

P&L

Using tail classes

Tail thickness classes and the FFT grid they size

numerics

severity

Using `tsallis`

The Tsallis distortion, a Beta mixture of TVaRs with a closed-form Gini index, and the extended calibration set

pricing

Using `tweedie`

Tweedie parameter conversions and named laws with the tweedie statement

distributions

Using unconditional layers

Conditional and unconditional layer severities, and the trailing ! on a severity

severity

Using validation

The validation verdict on a computed object, reinsured views, and the warning a failing build emits

numerics

output

reinsurance

Using FFT windows

The FFT grid window chosen by the bucket sizer, shown by bs_window_df

numerics

Using `yelt`

Aggregates from year loss tables with the yelt clause

catastrophe

Using `zm` and `zt`

Zero-truncated and zero-modified claim counts, and the two geometric distributions

frequency