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  3. Life Insurance Products Valuation in R

Exercise

The number of deaths

Cynthia's professor now asks her to explore the number of deaths in the life table. The deaths at age \(x\) are labeled \(d_x\). Can you picture the number of deaths \(d_x\) by age \(x\)?

Moreover, Cynthia learned that \(d_x\) is the expected number of people who die at age \(x\) out of a group of \(\ell_x\) survivors. You will generate binomial samples for the number of deaths at age \(x\) and compare simulated data with the registered \(d_x\).

The object life_table is preloaded in your R workspace as well as the extracted columns age, qx, lx and dx.

Instructions

100 XP
  • Plot dx versus age to examine the number of deaths by age. Using type = "h" you obtain vertical lines instead of points.
  • Simulate the number of deaths at each age \(x\) based on the number of survivors lx and the mortality rates qx. Use rbinom() to generate in a vectorized way from a binomial distribution.
  • Plot the simulated number of deaths sims on top of the existing graph using points(). Crosses are used as symbols by specifying pch = 4.