IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
Under a Gompertz model the force of mortality is μ(x) = B·c^x. Which statement about the force of mortality is correct?
Under Gompertz, the force of mortality is multiplied by the constant c each year of age, so when c exceeds 1 it grows exponentially. Equivalently, its logarithm is linear in age.
- AIt is constant in x
- BIt increases linearly with x
- CIt changes by a constant proportion for each additional year of age (when c > 1, it grows exponentially)Correct
- DIt decreases with age when c > 1
- Its logarithm is quadratic in x
Explanation
μ(x+1)/μ(x) = c, so the force changes by a constant factor each year, and for c > 1 it grows exponentially. Its log, ln B + x ln c, is linear in x, not quadratic.
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