IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting and valuing cashflows contingent on multiple decrement events
Which statement about dependent and independent decrement rates is correct for a life subject to two causes of decrement?
The dependent rate for a cause is never greater than its independent rate. Competing causes can remove a life before the cause in question acts, so the chance of leaving by that cause in the multiple decrement table is at most the rate in its single-decrement table.
- AThe dependent rate for a cause is never greater than the corresponding independent rateCorrect
- BThe dependent rate for a cause is always greater than the corresponding independent rate
- CThe dependent rates for all causes always sum to less than the independent rates
- DThe dependent and independent rates are equal whenever either force is positive
- Independent rates sum to the total decrement probability
Explanation
In the multiple decrement table, a life can leave via another cause before the given cause acts, which can only reduce the chance of leaving by this cause. Hence q_j^(τ) <= q_j'. The sum of dependent rates equals the total decrement probability, not the sum of independent rates.
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