Bahnemann Flashcards
Panjer’s Recursive Algorithm
Size view of losses
Layer view of losses
Expected losses in a layer
E[X; a; l] = E[X; a + l] - E[X; a]
Excess loss conditional on a claim exceeding retention
Mean residual life at a
Graphs of excess severity
Mean and variance of excess claim counts
p = probability that a loss exceeds a
Impact of inflation in fixed excess layer
Impact of severity inflation on excess counts
Impact of severity inflation on aggregate losses
Mean and variance of aggregate losses in a layer
Claim contagion parameter (accounts for claims not being independent of each other)
What the risk charge covers
Contingencies such as process and parameter risk
ILF assumptions
- All UW expenses and profit are variable and do not vary by limit
- Frequency and severity are independent
- Frequency is the same for all limits (may not be true due to adverse/favorable selections)
Price of a layer of coverage using ILFs
Consistency in ILFs
Increasing and doing so at a decreasing rate.
Premium for successive layers of coverage of constant width will be decreasing
Violation: adverse selection, lawsuits influencing size of limits (frequency would not be the same)
Risk loaded ILFs
Risk load: Miccolis approach
Risk load: ISO approach
Premium for policy with limit l and deductible d
Pure premium after inflation
LER relationship for the three different deductible types
Straight
Diminishing
Franchise
Franchise deductible
Loss is truncated but not shifted
Diminishing deductible
Advantage/disadvantage of Panjer’s
Good for small frequency of claims
Only a single severity distribution can be used
Issues with using lognormal distribution
No ability for loss-free scenario (ln 0 is undefined)
No easy way to reflect impact of changing per occurrence limits on aggregate limit
Theoretical curve fit for excess severity if curve is flat
Exponential
Theoretical curve fit for excess severity if curve is linear
Pareto
Theoretical curve fit for excess severity if curve is decreasing exponentially
Gamma
Theoretical curve fit for excess severity if curve curves up
Lognormal
Theoretical curve fit for excess severity if curve is concave down
Weibull
Issue with fitting excess severity curves
Data usually thin and volatile at the higher amounts – difficult to see a pattern
Pricing a layer of coverage and applying a risk load
Can’t simply subtract risk loaded ILFs (incorrect resulting risk load)
ILFs that account for both claim and aggregate limits
E[Sl;L] / (E[N] x E[X;b])
Impact of inflation on deductibles
ILF after inflation
ILF of the deflated limit DIVIDED by the ILF of the deflated basic limit
Basic pure premium after inflation
Freq x Sev x (1 + t) x deflated basic limit
