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Reasons for deviations from expected experience
- error of estimation
- deterioration or improvement of expected experience from unexpected influences
- statistical fluctuations
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Desirable characteristics of risk margin
- less is known about estimate, higher should risk margin be
- risks with low frequency and high severity should have higher risk margin
- contracts persisting over a longer timeframe should have a higher risk margin
- risks with a wide probability distribution should have higher risk margins
- to the extent that emerging experience reduces uncertainty, risk margin should decrease
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Desirable characteristics of risk margin methodology
- consistent methodology for the entire contract lifetime
- method and assumptions consistent with sound insurance pricing practices
- vary by product based on risk differences
- be easy to calculate
- be consistently determined between reporting periods and between entities
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Larger margin is appropriate if
- actuary has less confidence in the best estimate assumption
- approximation with less precision is being used
- event assumed is farther in the future
- potential consequence of the event assumed is more severe
- occurrence of the event assumed is more subject to statistical fluctuation
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3 categories of MfAD
- claims development: % of claim liabilities; 2.5% to 20%
- recovery from reinsurance ceded: % of ceded reinsurance, 0% to 15%
- investment return rates: deduction from investment rate, 0.25% to 2.00%
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Cases where margin can be higher or lower than bounds
- higher for unusually high uncertainty
- higher when resulting provision is unreasonably low because best estimate is low
- lower for investment return rate if initial rate is lower than 0.25%
- lower when reinsurer runoff where all treaties are commuted (low claim MfAD)
- lower for insurer with aggregate stop loss reserved at the stop loss limit
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Factors influencing the margin for claims development
- claims management: systems, personnel, guidelines, procedures
- operations: underwriting personnel, adequacy of staffing, guidelines for UW
- data on which estimate is based: volume, homogeneity, new exposure, mix of bus.
- line of business: environment (legislative / judicial / gov), length of tail, retention
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Factors influencing the margin for recovery from reinsurance ceded
- proportion of related party reinsurance
- ceded loss ratio and commission rate
- unregistered reinsurance
- reinsurers under liquidation or with weak financial conditions
- claim coverage disputes with reinsurers
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Factors influencing the margin for investment return rates
- mismatch risk between payment of claims and availability of liquid assets
- error in estimating the payment pattern of future claims
- asset risk including credit/default risk and liquidity risk
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Methods for calculating interest rate MfAD
- weighted formula: MfAD = iPM - min(iPM,iRFM x (1 - k))
- explicit quantification: asset/liability mismatch + timing + credit risk margins
- coverage ratio = (premium liability + claim liability) / (investment + instalment premium)
- A/L mismatch: coverage ratio* i * (DA - DL) / DL
- timing risk: L / (1 + d*)D = L / (1 + d)(1 - k)D, k = % change in D
- credit risk: yield curve of high quality bonds vs corporations
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Reasons to dismiss prescription around setting assumptions
- entails significant and time-consuming testing and review of industry data
- requires a large number of possible assumptions or variations to be covered
- difficult to anticipate all the unique company circumstances
- ranges would need periodic updating to reflect emerging experience
- undermines integrity and responsibility of the AA
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Quantile approaches
- multiples of σ: simplicity, practicality
- percentile or confidence level: most commonly applied (VaR)
- CTE: average outcome exceeding Qth percentile
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Evaluating quantile approaches
- the less is known about the current estimate and its trend, the higher the margin (σ,CTE)
- risks with low frequency and high severity should have higher risk margin (σ,CTE)
- contracts that persist over a longer timeframe should have higher risk margin (none)
- risks with a wide probability distribution should have higher risk margin (σ,CTE)
- to the extent that emerging experience reduces uncertainty, risk margin decreases (σ,CTE)
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