Actuary Certification Loss Models Flashcards
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The Panjer recursion formula is used to compute the aggregate loss distribution when frequency is in the (a, b, 0) class. It relates:
Answer: fs(x) to fs(x−1) using frequency probabilities and severity
Panjer's recursion computes fs(x) = Σ(a + b·y/x)·p(y)·fs(x−y), recursively building the aggregate distribution from frequency and severity.
Which loss distribution has the property that its hazard rate is constant, implying memorylessness?
Answer: Exponential distribution
The exponential distribution has a constant hazard rate λ, which is equivalent to the memoryless property: P(X > s+t | X > s) = P(X > t).
In the context of the exam STAM (Short-Term Actuarial Mathematics), which topic is NOT typically covered?
Answer: Life contingencies and survival models
Life contingencies and survival models are covered in Exam LTAM (Long-Term Actuarial Mathematics), not Exam STAM, which focuses on short-term loss models.
A deductible policy modification that changes the ground-up loss X into the per-payment variable Y = (X − d | X > d) results in which transformation of the CDF?
Answer: FY(y) = [FX(y+d) − FX(d)] / [1 − FX(d)]
The per-payment variable after deductible d has CDF FY(y) = [FX(y+d) − FX(d)] / S(d), a shifted and rescaled version of the ground-up CDF.
In maximum likelihood estimation for a censored and truncated sample, the likelihood contribution of an observation xi that is left-truncated at d and right-censored at u is:
Answer: [f(xi) / S(d)] for exact losses; [S(u) / S(d)] for censored
An exact loss at xi contributes f(xi)/S(d) and a right-censored observation at u contributes S(u)/S(d), both conditioned on the truncation point d.
Under the normal power (NP) approximation for aggregate losses, the skewness of the aggregate distribution is used to:
Answer: Correct the normal approximation by accounting for asymmetry
The NP approximation refines the normal approximation by incorporating the coefficient of skewness γ to capture the asymmetry of the aggregate loss distribution.