This component is used in the Capital Eagle model for the mtpl, motor hull and personal accident lines of business.

• Underwriting information
• Claims generators
• Sum insured allocator
• Reinsurance program
  

This component is used in the Capital Eagle model for the property line of business. The difference between this component and the example line of business are the additional event claims generators for the perils earthquake, storm and flood.

• Underwriting information
• Claims generators
  
• Sum insured allocator
• Reinsurance program
  

Compared with other lines of business, this component doesn't contain any reinsurance contracts. This component may be of use in a model with a global/ multiline reinsurance program.

• Underwriting information
• Claims generators

In motor third party liability possible risk bands might be i.e. private cars, taxis, trucks, petrol trucks. Each risk band is specified in an own table row containing the following information:

• maximal sum insured
• average sum insured
• premium
• number of policies

In case the parameterization contains surplus reinsurance treaties, the sum insured information and at least two risk bands are required. When using a surplus contract, it is also essential to select the allocation properties.

The following components are normally requesters of underwriting information:

• claims generators, as their calibration may be based on sum insured, premium, number of policies;
• frequency generators, as their calibration may be based on number of policies;
• sum insured to claims allocators;
• proportional reinsurance contracts as they need gross underwriting information in order to calculate the ceded underwriting information;
• working/cat excess of loss and stop loss reinsurance contracts, as the ceded premium may be specified as gnpi, rate on line and number of policies.

There are different ways of generating claims containing risk profiles:

• a claims generator per risk profile
• allocating a risk profile to a claim. The current allocator component offers three different strategies:
  
• none: if a parameterization has no surplus contracts, there is no sense to waste runtime by allocating claims to risk profiles
• risk to band
• sum insured generator

Detailed information on the later two strategies is available in a pdf.

Parameterization is done with a quantity structure describing the price per exposure unit, the written exposure and the used exposure base (i.e. absolute, written premium, number of policies, sum insured).

Usage in Models

• A line of business normally contains different kinds of claims generators, i.e. an attritional claims generator and a single claims generator or several event claims generator.
• If an event affects several lines of business, the event generator will rather be part of a cat model than of a single line of business.

generate one claim of type attritional per period. Attritional claims are covered by proportional reinsurance contracts such as quota share and surplus and stop loss contracts.

generate a certain number of claims of type single per period. The number is normally received from a frequency generator. Single claims are covered by proportional reinsurance contracts and the working excess of loss (WXL) and stop loss contract.

generate a certain number of claims of type event aggregate per period. The number is normally received from an event generator. Event aggregate claims are covered by proportional contracts, cat excess of loss (CXL) and stop loss contracts.

Common Parameterization Structure

Independent of the generated claim type the following parameters may be set: 

Base: Apart from an absolute parameterization it is possible to calibrate the claim size based on premium written, number of policies and sum insured. In a first step a random number is generated according to the selected distribution and parameters. This number is then multiplied with the ‘base’ value. If the underwriting information consists of several risk bands the selected base values will be added up.

Distribution: The following ‘distributions’ are included. Adding further distributions is easy.

• chi square quadrat
• constant
• discrete empirical
• discrete empirical cumulative
• inverse Gaussian
• lognormal (mean, standard deviation)
• lognormal (mu, sigma)
• negative binomial
• normal
• pareto
• poisson
• piece wise linear
• piece wise linear empirical
• student
• triangular
• uniform

Parameter labels will be are switched in the tree view, if a different distribution is selected.

Modification: There are several ways to modify the random value, namely to censor, shift or truncate.

Background Information on Random Numbers

We use the SSJ Library from the University of Montreal for random number generators. Currently all random number generators are using F2NL607.

Parameterization possibilities

Explanations on claim types

It is used currently used for the property line of business in the Capital Eagle model.

Parameterization possibilities

Explanations on claim types

In a first step the number of claims is generated using the frequency generator. This number is sent to the claims generator that will generate as many single claims as defined by the frequency generator.

Parameterization possibilities

Explanations on claim types

Base: Apart from an absolute parameterization it is possible to calibrate the frequency based on number of policies. In a first step a random number is generated according to the selected distribution and parameters. This number is then multiplied with the ‘base’ value. If the underwriting information consists of several risk bands the selected base values will be added up.

Distribution: The following ‘distributions’ are included. In general you will select a discrete distribution.

• chi square quadrat
• constant
• discrete empirical,
• discrete empirical cumulative
• inverse Gaussian
• lognormal (mean, standard deviation)
• lognormal (mu, sigma)
• negative binomial
• normal
• pareto
• poisson
• piece wise linear
• piece wise linear empirical
• student
• triangular
• uniform

Parameter labels will be switched in the tree view, if a different distribution is selected.

In the first step the number of claims is generated by using the frequency generator. Afterwards the event generator fetches the according number of event severities. Finally the claims generator generates the event claims using an inverse function.

Claim size parameterization possibilities

For the severities there are the same distributions as for the claims size available.

Explanations on claim types

Causal dependency modeling is possible using the same event to generate several claims in different lines of business.

Available are programs with a fixed number of serial ordered contracts or 'dynamic' programs allowing the user to add and remove contracts within the graphical user interface and to define the order in which they are applied.

The graphical user interface allows selecting a ‘strategy’ per contract. Currently implemented strategies are:

• quota share
• quota share with annual aggregate limit
• surplus
• working excess of loss
• cat excess of loss
• stop loss

• Each reinsurance contract is a template for any of the contracts available. The 'strategy' can be selected in the parameterization setting for different contract types.
• Net claims of contract 1 will be transfered to contract 2, in which those formely net claims will be interpreted as gross claims.
• The parameter insuring priority is not available in this program.

Additionally to this reinsurance program with a fixed order and number of contracts there is also a dynamic version available. The dynamic version provides the user a higher flexibility.

This reinsurance program is used in the Capital Eagle Model.

• In order to add an additional contract to the reinsurance program right click on reinsurance program and select 'Add'.
  
  
• To remove a contract, right click on it and select 'Remove'.
  
  
• Each reinsurance contract is a template for any of the available contracts available. The 'strategy' can be selected in the parameterization setting different contract types.
• The order of the contracts is defined with the parameter inuring priority.
  
• The contract with the smallest inuring priority will be the first executed. If several contracts have the same inuring priority they will be applied on the same 'gross' claims and underwriting figures.
  
• If a program has several excess of loss (XL) layers, add as many contracts as layers are required and set the inuring priority to an equal number.
  
• In order to keep a program flexible for extensions it makes sense to use i.e. 10, 20, 30 as priorities. These gaps allow to easily insert further contracts between already existing contracts.

• Dynamic multi line reinsurance programs have the same properties as dynamic reinsurance programs.
• Each contract has a 'covered lines' property as additional property. Double click on the list in order to select the covered lines using combo boxes.

Common parameters to all strategies are 

• covered by reinsurer defining the share signed
• Inuring priority is used if the user can add and remove contracts. It allows to define the order of applied contracts. Claims and underwriting information are first processed by the contract with the lowest inuring priority. The resulting net is then processed by the contract with the next higher inuring priority. If several contracts have the same inuring priority, they are applied in parallel. Parallel contracts may be used in combination with "covered by reinsurer" if a contract is splited among several reinsurers. Another use case consists of several XL layers.

Possible Strategies

• A quota share contract will have a proportional effect on all claim types.

By defining the reinsurer it is possible to model reinsurer defaults. The model should contain a reinsurer rating table and default probabilities per rating. If a reinsurer defaulti all contracts with this reinsurer will stop ceding claims.

If a contract is placed at different reinsurers, this can be done by selecting combinations of 'covered by reinsurer' and 'reinsurer'.

The finite reinsurance contract consists of two parts: An experience account and a risk part. This contract is a multi-period contract.

Input:

Model inputs:

For each period t, the finite re component receives list of claims C. These can be the ceded or the net claims produced by another reinsurance component. This has been decided by the model developer and cannot be changed by a model user.

User inputs: t refers to a time period

• the overall premium P(t) of the finite re contract in period t
  
• The fraction α(t) of the premium which is allocated to the experience account.
  

Output:

Experience Account

• premium P_ ea(t)
  
• claims C_ea(t)
  
• balance B(t) of the experience account
  

Risk Part:

• premium P_risk(t)
  
• claims C_risk(t)
  
• result R_risk(t) from the outset until the end of period t

Validation:

 none implemented, but should be

• P(t) > 0
• 0 =< α(t) =<1
  

Calculation:

• P_ea(t) = α(t) * P(t)
  
• P_risk(t) = (1 - α(t)) * P(t)
  

• C_ea(t) =  min(B(t-1) + P_ea(t), C(t)), if t-1 refers to a period before the start of the contract, then B(t-1) is set to 0
  
• C_risk(t) = C(t) - C_ea(t)
  

• B(t) = B(t-1) + P_ea(t) - C_ea(t). The definition of C_ea(t) ensures that the B(t) >= 0
• R_risk(t) = R_risk(t-1) + P_risk(t) - C_risk(t), if t-1 refers to a period before the start of the contract, then R_risk(t-1)  is set to 0
  

It is possible to generate the following claim types:

• attritional
• single
• event

Each claim consists of a value and a date. Ceded claims keep a reference to the original claim. Furthermore event claims have a reference to the event they belong too.

Actually the different claim types are required for reinsurance modeling as different contracts require different levels of information to calculate correctly the ceded part.

Reinsurance Coverage