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Handling Imbalance in FIE

1 Statement of Principles of Ratemaking

  • 4 principles of ratemaking? Evaluate a rate
    1. Rate \(= E(\text{Future costs})\)
    2. Rate provides for all costs associated with transfer of risk
    3. All costs associated with an individual risk transfer
    4. A rate should be...
      • reasonable
      • not excessive or unfairly discriminatory
      • \(\implies\) Actuarially sound estimate of \(E(\text{Future Costs})\)
      • (associated with individual risk transfer)
  • Considerations for Actuarially sound rates
    • Helps predict future costs? \(\implies\) Relevant
    • Subdividing data: homogenous groups with statistically reliable volume
    • Credibility attached to data. Credibility =\(f(\text{Homogeneity, Reliability})\)[^1]
    • Incorporate Reinsurance cost
    • Reflect all changes (internal/external) History \(\leftrightarrow\) Future
    • Higher Risk \(\implies\) Higher profit charge
    • Investment income \(\implies\) Higher profit charge
    • Judgements should be well-documented, available for disclosure
  • Actuarially sound? Based on Considerations?

2 Pricing Methods

  • Other options to balance?
  • Possible ratemaking methods
    • Guessing
    • Non-insurance data
    • Competitor rates
    • Industry data
    • Adjust Insurer's historical LR / PP to reflect future period *most common
  • Adjustments and their purpose
    1. Large events
    2. One time changes
    3. trending
    4. development
    5. Load for LAE
    6. Load for Profit
    7. Reinsurance costs
    8. Credibility

3 Notes

While solving, add stuff here that is not covered in the source text but is useful information to think about (or perhaps the same information in a fresh perspective)

  • Residual markets: safety net for insureds that are unable to find insurance in standard market. Risky individuals are assigned as per the market share of the insurance company (20% market share \(\implies\) 20% of the high risk individuals in the residual markets will be assigned to this company)
    • A #doubt There could be differences in the residual market mechanism between states. For example, State X could have less adequate residual market rates than State Y, and might thus assess more from each insurer in the state.
  • External influences to justify higher rates (State X > State Y)
    • Judicial Environment may vary between the states: Higher tendency for lawsuits (Texas)
    • Regulatory & Legislative differences. Laws may require State X to have higher coverage than the laws in State Y.
    • Method of handingling of guaranteed funds might vary. If State X has more insurer insolvencies, then more money needs to be collected.
    • Different economic variables: Labor costs may be higher in state X => higher claim costs.
    • Differences in residual market mechanisms: State X has less adequate rates
    • State premium taxes are higher in State X
    • Weather Patterns in state X.
  • For catastrophic events (like terrorism) consider
    • Provision for catastrophes in Indication
    • Catastrophes \(\implies\) Reinsurance
    • Is the Government recognizing it? (and perhaps ready to pay for it)
    • Larger volatility \(\implies\) Higher profit margin
    • What is the coverage provided for terrorists attacks? The clause change, incorporate that into your rates.
  • Why do we actually trend premiums?
    • Will premiums change over time? Yes they will, since they really just depend on the exposures written. So if more exposures are written then more premium will be charged, commensurately.
    • But then why do we trend? We do, for the change in the mix of business. What if a lot of risky insureds bought insurance and a lot of low-risk individuals left the company? This would lead to an increase in the premiums even for the same number of exposures written on average.
    • Thus, we have to trend the premiums in order to account for that change in the mix.
  • Why do we adjust for one-time changes?
    • We do so because let's say we take these two years
      • 2024: Premiums = X
      • 2025: Premiums = Y, Rate change +10%
      • 2026: Premiums = Z
      • 2027: Future policy period for which rates are being determined
    • Now, Z already reflects the +10% increase in the premiums as compared to 2025. Y may have partially, but X has not at all.
    • Okay. First, let's say we adjust for the one time change, so we would have...
      • \(1.1X + 1.05Y + Z\) as the premiums for given losses for the years 2024-26, say \(L\)
      • The loss ratio would then be \(\dfrac{1.1X + 1.05Y + Z}{L}\) and let's say this is \(70\%\) and our current rates have LR = \(65\%\) then we have to increase the rates by \(16.66\%\) (very simple example)
      • All good here.
    • If we don't make the adjustment however, we will have \(\dfrac{X+ Y + Z}{L}\) which would be (say) \(60\%\) and so we have to decrease the rates by \(8\%\) (\(65\% \to 60\%\))
    • Which doesn't make sense... this happened because we didn't adjust the past premiums to reflect the one-time changes.
  • Future period can also be referred to as Prospective Period #lingo
  • "Trend exposures (if they are inflation-sensitive)"
    • Think of exposures in this case as wages. Wages are definitely inflation-sensitive. So you have to adjust the money to get it to the current level.
    • That is what we mean by trending exposures.