Actuary Certification ACTUARY Actuarial Models 3

Question 1

A disability income policy pays $1,000/month while disabled. Using a multiple-state model, which transition intensity governs recovery from disability?

Accepted Answer

μ_da (disabled to active)

Answer

The recovery intensity μ_da governs the transition from the disabled state back to the active (healthy) state.

Question 2

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)?

Accepted Answer

θ

Answer

The mean-reverting drift pulls r toward θ, which is the long-run equilibrium (unconditional mean) of the process.

Question 3

In collective risk theory, the stop-loss premium for retention d equals which expression?

Accepted Answer

Both A and B are equivalent

Answer

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.

Question 4

Which property of the Pareto distribution makes it particularly useful for modeling heavy-tailed insurance losses?

Accepted Answer

Slowly decaying power-law tail

Answer

The Pareto distribution's power-law tail F̄(x) ~ x^{-α} decays slowly, capturing rare but extremely large losses.

Question 5

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?

Accepted Answer

q'_x^(j) is the probability of decrement j in a world where only cause j operates

Answer

The associated single-decrement probability q'_x^(j) is defined in a hypothetical world where only decrement j is active, eliminating competing risks.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification ACTUARY Actuarial Models 3