# Long Term Reinsurance Buying Strategies modelled using a component based DFA Tool

```Long Term Reinsurance
modelled using a component
based DFA Tool
Astin July 2001
BENFIELD GREIG
Introduction
Investigate possible reinsurance strategies over several years.
Two Strategies:
• Constant Cover, but vary premium spend.
• Constant Spend, but vary cover purchased.
Use Monte Carlo Simulation to evaluate Risk / Return for an
example company.
Reinsurance Pricing Factors
• Many potential ways to model changes in reinsurance
pricing
• Various factors including:
 Loss Experience
 Changes in exposure
 Reinsurance Market conditions
• The method used here is based on Loss Experience, with
exposure and market factors assumed to be constant.
Example Company
Example model is a property Cat XL programme with the
following parameters (USD million):
120
 Expenses
30
 Small Claims
48
 Large Cat Loss Freq Poisson distribution with mean 1.
• Large Cat Loss Size Lognormal distribution, mean 12,
standard dev. 16.
Example Company Reinsurance
• The reinsurance programme consists of 4 layers as follows:
• (USD million)
Limit
10
20
50
50
Deductible Midpt
Initial ROL
20
25
11.6
30
40
6.9
50
75
3.4
100
125
1.9
• All layers have 1 reinstatement at 100%.
• Initial coinsurance for all layers is 25%.
Different Strategies
• Each Layer considered Separately
• In Constant Cover strategies, coinsurance is fixed and
• In Constant Spend strategies, coinsurance varies to keep
Change in Reinsurance Pricing
• The price of each layer in the reinsurance programme will
vary, with an increase in price if the experience account (EA)
for the layer is negative, and a reduction in price if the EA is
positive and there are no losses in the previous year.
• EA = reinsurance premiums and reinstatements – recoveries
• if EA &lt; 0 then premium = previous premium + EA * 10%
• if EA &gt; 0 then rate = previous rate * 90%
• Initial EA = 0.
Change ROL over time - Total Loss in Year 3
0.20
0.18
0.16
ROL
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0
1
2
3
Year
4
5
6
Model Implentation
• Modelled Using ReMetrica II
• Component Based Framework for risk analysis and DFA (
Dynamic Financial Analysis )
• Main Uses Include:
– Reinsurance Pricing and Strategy
– Risk Based Capital Modelling &amp; Capital Allocation
The Model
Results
• The graphs below show the cedant’s net underwriting result.
As a measure of risk we show:
 Standard Deviation
 1 in 100 result
 Probability of a negative UW result
• As a measure of return we use expected UW result.
• The numbers on the graph indicate the years 1 – 5.
Results
• The results were based on 20,000 simulations using
stratified sampling of 10,000 strata
• Performed sensitivity testing with further simulations (
50,000 ) and different parameters.
Risk Return - Standard Deviation
Reinsurance Strategy - Risk Reward
29.40
5
5
29.20
29.00
4
4
28.80
28.60
28.40
12.4
3
3
2
12.6
12.8
13.0
13.2
13.4
1
13.6
2
13.8
14.0
Net UW Result (USD mill) - Standard Deviation
Const Cover,Property,Net Underwriting Result
Const Spend,Property,Net Underwriting Result
Risk Return - 1 in 100
Reinsurance Strategy - Risk Reward
5
5
29.30
29.20
29.10
29.00
4
28.90
4
3
28.80
3
28.70
2
28.60
2
1
-19
-18
-17
-16
-15
28.50
-14
Net UW Result (USD m ill) - 1st Percentile
Const Cover,Property,Net Underwriting Result
Const Spend,Property,Net Underwriting Result
-13
-12
28.40
-11
Risk Return - Probability Loss
Reinsurance Strategy - Risk Reward
29.30
5
5
29.20
29.10
29.00
28.90
28.80
4
4
3
3
28.70
2
28.60
2
28.50
28.40
3.2%
3.4%
3.6%
3.8%
4.0%
Probability negative Net UW Result
Const Cover,Property,Net Underwriting Result
Const Spend,Property,Net Underwriting Result
1
4.2%
4.4%
Conclusions
• Constant Spend strategy better than Constant Cover
Strategy.
• Return appears similar, but risk is less.
• Consistent across different risk measures.
Relevance
• Constant Spend strategy is similar to the following strategy:
– Buy core programme down from a top PML ( probable
maximum loss ) figure and buy lower down on an
opportunistic basis.
• Opposite strategy reduces reinsurance when cost is low and
buys more when costs are high. I call this the ‘short memory’
strategy.
• Constant Cover is neutral.