reinsurance cover

Importance of Reinsurance Cover (Statistical Evidence)

Ashish Chaturvedi
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What is Reinsurance:

Every Insurer must pay out legitimate claims as a basic promise of the insurance contract. There are several ways in which insurers seek to hedge this liability. Most common and traditional way is to reinsure, which means insurers find a reinsurer to either

  1. accept insurer’s risks on proportional basis (a % of risk is transferred defining the premiums and claims portions for reinsurer on each risk) , called a quota share or
  2. accept insurer’s losses on each risk when they exceed a certain threshold, called the retention amount
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Both the above methods are effective with each one having its own benefits and challenges. There are other methods too but not required for the purpose of this article. Based on insurer’s strategy of the reinsurance program design, they generally adopt a combination of these methods in their reinsurance program. Any insurer which has a well thought out reinsurance program design would always need analysis of what is the claim frequency and severity for the past several years.

To model claims frequency, discrete random variable analysis is done with which insurers can model the probability distribution (probability mass function) to model all values that claim frequency could take.

To model the claim amounts, continuous random variable analysis is adopted with which insurers can model the probability density functions to model the claim amounts

Modeling for Claims:

The whole intention of insurers, while they analyze the past claims and try to predict future losses (exploratory data analysis) is the differentiation between a sample and a population in statistics. This is essential to understand because the aim of this analysis is to draw informed conclusions about unknown values for a population-based on the observed data in the sample.

Following models commonly arise out of Claim Frequency analysis

  1. Poisson
  2. Uniform
  3. Binomial
  4. Bernoulli
  5. Geometric
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Following models commonly arise out of Claim Severity analysis

  1. Pareto
  2. Exponential
  3. Normal
  4. Log normal
  5. Gamma
  6. Weibull

Scenario

A claim amount random variable is uniformly distributed over an interval (0,700), which means that the maximum claim amount the insurer gets is limited to 700. The insurer has an excess of loss reinsurance arrangement (option (b) listed above) under which insurer retention is 600 on each claim. Let’s see what happens when the insurer has a reinsurance cover and what if it doesn’t

Insurer doesn’t have reinsurance cover:

Average claim amount for insurer= 700-0/2= 350

Variance = (700-0)^2/12 = 40,833

Insurer has reinsurance cover:

Average claim amount for insurer (E(Y))= Integral of x* 1/700 for claims up to 600 + Integral of 600*1/700 for claims over 600 up to 700

=343

Variance = E(Y^2)-[E(Y)]^2 = 36,637

This proves statistically that having the above reinsurance cover reduces the average claim amount and the variance of the claims.

References