To survive or not to survive
Cynthia is 20 years old and joins the actuarial department of an insurance company for a summer internship. As a first challenge Cynthia’s supervisor asks her to compare the (expected) present values of a pure endowment on the one hand versus a guaranteed payment on the other hand.
In this chapter you will always work with the 1999 period life table for females in Belgium of which the one-year survival probabilities \(p_x\) have been preloaded as px. For this exercise you will consider a single payment of 10,000 EUR and a constant interest rate \(i = 2 \%\).
This exercise is part of the course
Life Insurance Products Valuation in R
Exercise instructions
- Compute the
PVof a guaranteed payment of 10,000 EUR in 5 years from now at a rate of 2%. - Define
kpxas the 5-year survival probability \(_5p_{20}\) of (20) by taking the product over the subset ofpxcorresponding to ages 20 to 24. - Multiply
PVwithkpxto obtain the expected present value of a pure endowment of 10,000 EUR in 5 years from now for 20-year-old Cynthia.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# PV of guaranteed payment of 10,000 in 5 years
PV <- ___ * (___) ^ ___
PV
# 5 year survival probabilities of (20)
kpx <- ___(px[(___):(___)])
# EPV of pure endowment of 10,000 in 5 years for (20)
___