CARe Limited Attendance Seminar

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CARe Limited Attendance Seminar

• Some Practical Considerations for Catastrophe
  Aggregate Distribution Modeling

Peter R. Martin, FCAS Axis Specialty
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• Two Facts
• All commercially available cat models have
  portfolio management modules
• None of these models provide a true portfolio
  management system

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What Do I Mean By This?

• May not provide for consideration of some treaty
  typese.g. retro, stop loss, per risk, etc.
• No consideration of risk-attaching pro-rata
  treatiespotential losses above single treaty
  year event limit
• No ability to easily model prospective
  portfolios, e.g January 03 in-force as at
  December 02
• Portfolio optimization routines difficult to run
  within the models
• Difficult to test alternative frequency
  distributions for annual aggregate analysis, e.g.
  negative binomial for European Wind
• Linking portfolio modeling to pricing selections
  cumbersome

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Implication

• Reinsurers need to develop their own portfolio
  management application, which
• Integrates with financial, pricing, and cat
  modeling systems
• Is fast
• Is flexible

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Possible Process

• For each program, create a vector of ground up
  losses for a specific, fixed set of events
• Use any cat model
• Record expected loss by peril for each contract
  (extract from pricing system)
• Iteratively solve for scalars which (when applied
  to ground up loss vector) generate target
  expected loss cost to each layer by peril
• Store vector and scalarsContract vectors form
  matrix which, when multiplied by vector
  representing company participation produces a
  vector representing company cat loss distribution
  for each peril

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By Peril

5 Events
5 Contracts
Participations
Loss Dist
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Pictorial Representation of Process
Excel Pricing Application
Data Store
Severity Distribution
Annual Aggregate Distribution
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Hard PartThe Scaling Routine

• Scaling one of the perils can lead to other
  perils getting out of balance (on limited
  reinstatement contracts)
• Approach

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Ground up vector
Default Scale Factor
Scaling
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Advantages

• Fast
• Can scale, accumulate large portfolio in under 30
  minutes using off the shelf database products and
  high spec processor
• Quick enough to provide real-time incremental
  pricing analysis
• Flexible
• Most every type of cat exposed business can be
  analyzed, all you have to do is develop the
  vector of losses
• Easy to add/remove contracts to analysisperfect
  for optimization routines
• Simple integration with DFA analysis
• Can use FFT/Panjer/Simulation to develop annual
  aggregate distributions under various frequency
  assumptions
• Consistent
• Produces results that tie with pricing analysis

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Disadvantages

• Logic Flaws
• Why apply a different scale factor to ground-up
  losses for different contracts in the same
  program?
• Scaling can conceivably lead to higher layers
  having limit losses (for a given event) while
  lower layers have partials
• Multiple Models
• Doesnt explicitly address the fact that
  different models have different shaped curves
• Implicitly considered through blended selection
  of E(L)
• Requires more guesswork from underwriters
• Underwriters need to select expected loss by
  perilis this reasonable?
• May lead to abuse, e.g. understating hurricane
  E(L) to make incremental loss analysis less
  punitive
• Scenario analysis more difficult