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Reinsurance

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WORK IN PROGRESS: This manual contains descriptions needed by users and developers.

1. Reinsurance Overview

Reinsurance contracts are usually grouped in a reinsurance program. It is possible to model reinsurance programs per line of business, global reinsurance programs with multi line coverage or a mixture of both concepts.

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
 

2. Reinsurance Program

This reinsurance program has a fixed number of three reinsurance contracts. Contracts are processed in serial order.
  • 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.

3. Dynamic Reinsurance Program

A dynamic reinsurance program enables the user to specify the number and order of contracts with the parameterization.
  • In order to add an additional contract to the reinsurance program right click on reinsurance program and select 'Add'.
    Add Reinsurance Contract
  • To remove a contract, right click on it and select 'Remove'.
    Remove Reinsurance Contract
  • 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.

 

If a model shouldn't allow a user to edit the number and order of contracts there are also programs with a fixed number and order available.

4. Dynamic Multi Line Reinsurance Program

A dynamic multi line reinsurance program is not part of any line of business. However, the dynamic multi line reinsurance program is usually attached on the same level as lines of business in the model tree.
  • 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.

5. Reinsurance Contract

Each reinsurance contract has a strategy defining the contract type.

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.
 

6. Multi Line Reinsurance Contract with Default

This contract allows to define the covered lines and the reinsurer as counter party of the contract.

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'.

7. Finite Reinsurance

Multi-period contract with an experience account and a risk component.

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

 

 Finite Re contract output

 

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)
Both of these values are deterministic since α and the total premium P are fixed, deterministic values.

 

  • 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
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