4. Life Contingencies

Multiple Decrement — Quiz

Test your understanding of multiple decrement with 5 practice questions.

Practice Questions

Question 1

In a multiple decrement model, if the forces of decrement are constant over a short interval, what is the relationship between the dependent probability of decrement for a specific cause and its corresponding independent probability of decrement?

Question 2

Consider a multiple decrement model with two decrements: death (d) and withdrawal (w). If the force of mortality is given by $\mu_x^{(d)} = 0.02$ and the force of withdrawal is given by $\mu_x^{(w)} = 0.03$. Assuming constant forces over the year, what is the probability that an individual aged $x$ will survive all decrements for one year?

Question 3

In the context of multiple decrement models, what is the primary purpose of an 'associated single decrement table'?

Question 4

If $\mu_{x+t}^{(1)}$ and $\mu_{x+t}^{(2)}$ are the forces of decrement for causes 1 and 2, respectively, what is the probability that an individual aged $x$ will experience decrement 1 between ages $x+t$ and $x+t+dt$, given survival to age $x+t$?

Question 5

In a multi-state valuation framework, what is the primary advantage of using a continuous-time model over a discrete-time model for multiple decrements?