Insurance Models Flashcards
7 cards from real Actuary Certification practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Insurance Models flashcards as text
In the collective risk model, what does the aggregate loss S = X1 + X2 + ... + XN represent?
Answer: Sum of individual claim severities over a random number of claims
S is the aggregate loss formed by summing N individual claim amounts, where N is a random claim count variable.
Which distribution is used to model the time between successive claim arrivals in a Poisson process?
Answer: Exponential
Inter-arrival times in a Poisson process are exponentially distributed with the same rate parameter λ.
A stop-loss reinsurance treaty pays losses exceeding a retention d. The net stop-loss premium equals:
Answer: E[max(S − d, 0)]
The stop-loss premium is the expected value of the excess loss above the retention, E[max(S−d,0)].
The coefficient of variation (CV) of aggregate losses S is lower than the CV of individual claim severity X when:
Answer: There are many independent claims (large n)
By the law of large numbers, pooling many independent claims reduces relative variability, lowering the CV of S compared to X.
Under the individual risk model, the total loss for a group of n independent policies is modeled as:
Answer: S = b1·I1 + b2·I2 + ... + bn·In where Ii are Bernoulli indicators
The individual model sums fixed benefit amounts bi scaled by Bernoulli claim indicators Ii for each policy.
What is the primary advantage of using the recursive (Panjer) formula for aggregate loss distributions?
Answer: It efficiently computes the aggregate distribution when (a,b,0) claim counts are combined with discrete severities
Panjer recursion exploits the (a,b,0) property of N to compute aggregate probabilities iteratively without full convolution.
In insurance pricing, the pure premium is calculated as:
Answer: Expected losses divided by earned exposure units
The pure premium equals E[aggregate losses] / E[exposure], representing the expected loss cost per unit of exposure.