A life insurance plan for Miss Cathleen
Cynthia helped Miss Cathleen while she was an intern with a life insurance company. Now, Miss Cathleen, aged 48, seeks for financial protection in case she would die around her retirement. To protect her growing-up children she wants to insure a benefit of 40,000 EUR for death between age 55 and 75, as shown below.
To value this temporary life insurance plan you will once again use the 1999 Belgian female life table, of which the one-year survival probabilities px and mortality rates qx have been preloaded. The assumed interest rate of 5% is available as i.
本练习是课程的一部分
Life Insurance Products Valuation in R
练习说明
- Calculate the deferred mortality probabilites \(q_{48}, \: _{1|}q_{48}, \: \ldots, \: _{26|}q_{48}\) of a 48-year-old up to age 75 as the product of multi-year survival probabilities and mortality rates.
- Define the appropriate discount factors at rate
i. - Specify the
benefitsvector as the death benefits of this temporary life insurance. - Compute the expected present value of the plan.
交互式实操练习
通过完成这段示例代码来试试这个练习。
# Deferred mortality probabilites of (48)
kqx <- c(___, ___(px[(___):(___)])) * qx[(___):(___)]
# Discount factors
discount_factors <- (___) ^ - (1:length(kqx))
# Death benefits
benefits <- c(rep(___, ___), rep(___, length(kqx) - 7))
# EPV of the death benefits
EPV_death_benefits <- ___
EPV_death_benefits