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Large Events

Anomalies

Example of Shock

  • Total loss on a large home
  • The CEO gets hypothermia

Definition of Shock Varies

  • Though they have predefined definitions
  • They differ by insurer and LOB
  • Due to size of book of business
    • 1M loss has huge impact where annual prem is 10M
    • But not for one which has 1000M as annual prem

What if you don't adjust?

  • Most years have $500,000 (LUCKY)
  • Some years will have $2,000,000 (UNLUCKY)
    • Usual $ 500,000 + additional $ 1,500,000

In general, if you don’t adjust for shock losses or catastrophes in your historical loss data, you will

  • overestimate future expected losses when these events are in your dataset, and
  • underestimate future expected losses when the events do not occur in your dataset.

GOAL: Produce rates that cover these costs over a long period of time, and don't overreact to unlucky years

Adjustments to Shock Losses

Cap at basic limits (liability)

  • Rate only for basic limits
  • Separately price for others
  • Workers comp doesn't have limits (doesn't work!)

Cap losses & apply XS load (property)

  • Cap all (Non-XS)
  • Calculate an XS-loading: \(1 + \dfrac{\text{XS Losses}}{\text{Non-XS Losses}}\) (read #Notes about definition of Excess)

Remove ground-up & load for XS (less common)

Selections

Cap Levels

  1. AJ
  2. Percentile of size of loss distribution
  3. Loss as % of insured value

Number of years to choose

Goal

To balance stability of the average and its (average's) responsiveness to changes.

  • Too less years, unstable
  • Too many years, not identifying latest patterns at all

Inflation / Changes in Avg Severity

Use this as the XS loss factor

\[ \dfrac{\text{Trended XS Losses}}{\text{Trended Non-XS Losses}} \]

Adjustments to Cat Losses

  1. Project AIY / Exposure
  2. Non-Modelled Cat Provision per AIY
    • \(= \text{Arithmetic Avg cat/AIY} \times \text{ULAE Factor}\)
  3. Non-Modelled Cat Pure Premium

What do we put in the numerator of our RL indication? Average Values! So, find the Non-Modelled Cat per exposure.

Notes

  • Excess can be defined in two ways:
    • the claims above 500k (The entire claim considered)
    • the amount above 500k (Only the excess portion considered)
  • Explanation:
    • Suppose you have 5 claims: \(N_{1}, N_{2},N_{3},E_{1},E_{2}\) where \(N_{i}\) are claims less than 500k and \(E_{j}\) are above 500k.
    • If we define excess as claims above 500k then
      • Excess amount: \(E_{1}+E_{2}\) (CONSIDER THE ENTIRE CLAIM)
      • Non-excess amount: \(N_{1}+N_{2}+N_{3}\)
    • If we define excess as the amount above 500k
      • Excess amount: \((E_{1}-500k) + (E_{2}-500k)\) (CONSIDER ONLY EXCESS PORTION)
      • Non-excess amount: \(N_{1}+N_{2}+N_{3}+500k\times 2\)