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Chapter 9

Mathematical Structure of Reinsurance: The Wisdom of Sharing Risk

#Reinsurance#Retention#Proportional Reinsurance#Excess of Loss (XOL)

Reinsurance: Insurance for Insurers

What happens if a massive typhoon strikes or a large fire occurs, requiring an insurer to pay more in benefits than it can handle? Insurers transfer part of their risk to other insurers, which is called Reinsurance. This is a key tool for improving capital efficiency and reducing the risk of insolvency.

1. Basic Structure of Reinsurance: Retention and Cession

  • Retention: The amount for which the primary insurer remains responsible.
  • Cession: The amount transferred to the reinsurer.
1
Primary Contract

The insurer takes on risk from customers and receives premiums.

2
Risk Assessment

Identify the portion of the assumed risk that exceeds capital strength.

3
Reinsurance Cession

Transfer the identified risk to a reinsurer and pay reinsurance premiums.

4
Recovery on Loss

If a loss occurs, receive benefit support from the reinsurer according to the ceded portion.

2. Two Main Types of Reinsurance

Reinsurance is broadly divided into two types based on how risks are shared:

Comparison of Proportional vs. Non-Proportional Reinsurance

CategoryProportional ReinsuranceNon-Proportional Reinsurance
Sharing MethodDivide premiums and losses by a fixed percentage (%)Reinsurer covers only the portion exceeding a certain amount (Retention)
Main TypesQuota Share, SurplusExcess of Loss (XOL), Stop Loss
Key FeatureFair distribution of profits and lossesExcellent defense against catastrophes
Premium CalculationDetermined proportionally to the primary premiumDetermined through specific actuarial probability models

3. Visualizing Risk Distribution

The following pie chart shows the share of the burden between the insurer and reinsurer according to the size of the accident when a non-proportional (XOL) contract is in place.

Example of Excess of Loss (XOL) Burden Sharing

In case of a $10M loss, the primary insurer retains $2M and the reinsurer covers $8M.


💡 Professor’s Tip

Reinsurance has a global network. Risks in one country are distributed to reinsurance markets in Europe or the US. The reinsurance system is the global implementation of the investment principle: “Don’t put all your eggs in one basket.”

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