ACTUARY Actuarial 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 ACTUARY Actuarial Models flashcards as text
An actuary models claim counts with a zero-inflated Poisson (ZIP) distribution. What parameter is added beyond the standard Poisson λ?
Answer: A mixing probability p representing the proportion of structural zeros
The ZIP model adds probability p of a structural zero (no claim ever), with the remaining 1−p mass following a standard Poisson(λ) distribution.
The Wang transform in risk pricing applies a distortion g(u) = Φ(Φ⁻¹(u) + λ) to the survival function. What does increasing λ accomplish?
Answer: Increases the risk loading, assigning higher weight to tail events
A larger λ shifts the survival function upward via the distortion, placing more weight on adverse outcomes and thus increasing the risk-adjusted premium.
Under the force of interest δ, the present value of a payment of 1 due in t years equals which expression?
Answer: e^(−δt)
With a constant force of interest δ, the present value factor is e^(−δt), the continuous-time discount function.
In a multiple-life model, the joint-life status (xy) fails at which time?
Answer: The minimum of T_x and T_y
The joint-life status fails as soon as the first life dies, so its future lifetime is min(T_x, T_y).
In simulation of insurance losses, the inverse transform method generates a random loss X from CDF F by computing which expression?
Answer: X = F⁻¹(U) where U ~ Uniform(0,1)
The inverse transform method sets X = F⁻¹(U) for a Uniform(0,1) variate U, guaranteeing that X follows the desired distribution F.
The expected shortfall (CVaR) at confidence level α for a loss variable S is defined as which quantity?
Answer: The expected loss given that the loss exceeds VaR_α
CVaR (Conditional Value at Risk) is the expected value of losses that exceed the VaR threshold, capturing average tail severity.
A term insurance pays benefit b at the end of the year of death if death occurs within n years. Using the equivalence principle, net annual premium P satisfies which equation?
Answer: P·ä_{x:n|} = b·A^1_{x:n|}
The equivalence principle sets the APV of premiums P·ä_{x:n|} equal to the APV of benefits b·A^1_{x:n|}, where A^1 denotes term insurance.