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METODOLOGÍAS Y PRÁCTICAS EN RESERVAS TÉCNICAS

PARA SEGUROS DE SALUD Y SEGUROS GENERALES

LIMA - 31 DE MAYO, 2007APESEG

Presentado por: APESEG & Milliman, Inc.

■ Advantages and LimitationsAdvantages and Limitations ■

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RESERVING METHODS IN PRACTICE

UK Survey - Projection Methods used in Practice

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Chain ladder

Bornhuetter-Ferguson

Loss Ratio x Premiums

Average Cost Per Claim

Exposure-based method

Inflation Adjusted Average Cost Per Claim

IBNR to Case Reserve Ratio

Inflation-adjusted chain ladder

Regularly Less frequently Once in a blue moon

Source: Claims Reserving Working Party Paper

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EXPLORATORY DATA ANALYSIS

Rate of Development

Smoothness of Development

Presence (absence) of Large Losses

Volume of Data

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EXPLORATORY DATA ANALYSIS

Appropriate Projection Methodologies

Anomalies in the data

Questions to ask management concerning issues manifested in the data

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ANALYST RESPONSIBILITIES

Recognize normal levels of random fluctuation

Recognize aberrations in loss development patterns

Recognize trends in loss development patterns

Question management concerning patterns

Identify underlying causes of aberrations

Make adjustments/corrections as necessary

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SENSITIVITY TESTS

Optimistic/Pessimistic Loss Development Factor Selections

Optimistic/Pessimistic Tail Factor Selections

Optimistic/Pessimistic Bornhuetter-Ferguson Expected Loss Estimates (Loss Ratios)

Different Weighting among methods

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WHEN THINGS GO WRONG

Management reviews the prior year actuarial report and fires claims manager because case reserves develop upwards over time

New claims manager instructs staff to reserve all claims at probable maximum amount

This results in an average 10% increase in the average outstanding reserve along the last diagonal

What will happen to the incurred loss development method?

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COMPARISON BEFORE AND AFTER STRENGTHENING

Ultimate Reserve Ultimate DifferenceAccident Cumulative Before Before After as Percent

Year Paid Strengthening Strengthening Strengthing Difference of Reserve2000 78,224 82,372 4,148 82,787 415 10%2001 81,287 87,511 6,224 88,568 1,057 17%2002 66,402 70,499 4,097 71,469 969 24%2003 62,347 80,394 18,047 82,841 2,447 14%2004 62,832 92,156 29,324 96,247 4,091 14%2005 33,568 64,040 30,472 68,134 4,094 13%2006 11,346 44,467 33,121 48,495 4,028 12%

Total 125,433 17,101 14%

Case Reserve Strengthening had a leveraged impact on the reserve –

Reserves overstated by 14%

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WHEN THINGS GO WRONG

Management pushes claims department to settle more claims

In 2006, claims department settled an additional 10% of claims (at the average outstanding + IBNR reserve)

What will happen to the paid loss development method?

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COMPARISON BEFORE AND AFTER ACCELERATION

Settlement acceleration had a leveraged impact on the reserve –

Reserves overstated by 31%!

Ultimate Reserve Ultimate DifferenceAccident Cumulative Before Before After as Percent

Year Paid Acceleration Acceleration Acceleration Difference of Reserve2000 78,459 80,571 2,112 80,812 242 11%2001 81,782 86,232 4,451 87,017 785 18%2002 67,183 74,210 7,027 75,534 1,324 19%2003 63,771 76,582 12,812 79,111 2,529 20%2004 65,846 92,968 27,122 98,974 6,006 22%2005 36,982 67,706 30,724 76,556 8,851 29%2006 14,676 44,643 29,967 60,282 15,640 52%

Total 114,215 35,376 31%

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LOSS RATIO

Implicit Assumption─Loss Ratio is known or can be reasonably estimated─Ultimate Loss is proportional to exposures (premium)

Strengths─Simplicity─Basic data requirements─Can use Pricing Assumptions concerning Loss Ratio

Weaknesses─Depends entirely on quality of Loss Ratio estimate

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PAID LOSS DEVELOPMENT

Implicit Assumption─Losses are paid at the same rate regardless of

accident year

Strengths─Simplicity─Basic data requirements─Does not depend upon case reserves─Provides objective test of incurred loss development

Weaknesses─Sensitive to changes in rate of settlement─Results for immature year may be erratic

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INCURRED LOSS DEVELOPMENT

Implicit Assumption─Strength of case reserves is dependent only on the

delay from accident date

Strengths─Simplicity─Basic data requirements─Converges to ultimate faster than paid method─May be better than paid for immature years

Weaknesses─Sensitive to changes in case reserve adequacy

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BORNHUETTER-FERGUSON

Implicit Assumption─Reserve is dependent upon the loss ratio, exposures,

and development pattern

Strengths─Combines loss ratio method with development

method─Avoids problem with development method instability

for immature years─Good to use when data are erratic

Weaknesses─Dependent on the quality of the loss ratio─Requires data on exposures as well as triangle data

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STRENGTHS / WEAKNESSES

Methods are intuitive – once data is arranged in triangle patterns become obvious

No sophisticated mathematics involved

Spreadsheets can be used

Data requirements are reasonable

Relies on implicit assumptions – may not be true

Failure of implicit assumptions may result in dramatically incorrect results

Too many parameters – fit data well but result in large variance in predictions

No information available on reliability of fit or error distribution

Haven’t really modeled the underlying process

Strengths Weaknesses