Actuary Certification ACTUARY Actuarial Models 2

Question 1

Under the Cox-Ingersoll-Ross (CIR) model, which property ensures interest rates remain non-negative?

Accepted Answer

The condition 2αθ ≥ σ²

Answer

The Feller condition 2αθ ≥ σ² ensures the process never reaches zero, keeping rates non-negative.

Question 2

In a select-and-ultimate mortality table, what does the 'select' period represent?

Accepted Answer

The initial period when recent underwriting affects mortality

Answer

The select period captures the effect of recent underwriting or selection, during which mortality differs from the population average.

Question 3

A compound Poisson process has Poisson frequency λ and severity distribution F(x). What is the variance of aggregate losses?

Accepted Answer

λ·E[X²]

Answer

The variance of a compound Poisson process equals λ·E[X²], which combines frequency variance and second moment of severity.

Question 4

Which interpolation method for fractional ages assumes a uniform distribution of deaths (UDD)?

Accepted Answer

Linear interpolation of l_x

Answer

Under UDD, the number of survivors l_{x+t} is linear in t between integer ages, implying a uniform distribution of deaths.

Question 5

In the Black-Scholes framework, what is the risk-neutral drift of a non-dividend-paying stock?

Accepted Answer

The risk-free rate r

Answer

Under the risk-neutral measure, all assets earn the risk-free rate r, replacing the real-world drift μ.

Actuary Certification Practice Test