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.
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A disability income policy pays $1,000/month while disabled. Using a multiple-state model, which transition intensity governs recovery from disability?
Answer: μ_da (disabled to active)
The recovery intensity μ_da governs the transition from the disabled state back to the active (healthy) state.
Under the Vasicek interest rate model, the short rate r(t) follows dr = α(θ−r)dt + σdW. What is the long-run mean of r(t)?
Answer: θ
The mean-reverting drift pulls r toward θ, which is the long-run equilibrium (unconditional mean) of the process.
In collective risk theory, the stop-loss premium for retention d equals which expression?
Answer: Both A and B are equivalent
The stop-loss premium E[max(S−d,0)] equals E[S] − E[min(S,d)], so both expressions A and B are equivalent definitions.
Which property of the Pareto distribution makes it particularly useful for modeling heavy-tailed insurance losses?
Answer: Slowly decaying power-law tail
The Pareto distribution's power-law tail F̄(x) ~ x^{-α} decays slowly, capturing rare but extremely large losses.
In a multi-decrement table with causes of decrement j=1,2,...,m, what is the relationship between the single-decrement probabilities q'_x^(j) and the associated single-decrement tables?
Answer: q'_x^(j) is the probability of decrement j in a world where only cause j operates
The associated single-decrement probability q'_x^(j) is defined in a hypothetical world where only decrement j is active, eliminating competing risks.
Under the lognormal model, if ln(S_T/S_0) ~ N(μT, σ²T), what is E[S_T]?
Answer: S_0·e^(μT + σ²T/2)
For a lognormal variable, E[S_T] = S_0·exp(μT + σ²T/2), applying the moment generating function of the normal distribution.
The Kolmogorov forward equations in a Markov chain model describe which relationship?
Answer: How occupation probabilities evolve forward in time as a function of transition intensities
The Kolmogorov forward equations express the time derivative of transition probabilities p_{ij}(t) in terms of the current state j and its outgoing intensities.