ACTSC232 Study Guide - Quiz Guide: Exponential Distribution, Random Variable, Life Insurance

• School: University of Waterloo
• Department: Actuarial Science
• Course: ACTSC232
• Professor: Johnny Li

Document Summary

1. (a) it is a fully-continuous whole life insurance contract. A death bene t of ,000 is payable at the moment of death. Premiums at a rate of per year are collected continuously from the policyholder until the moment of death. (b) setting e(l0) = 0, we have 10000 ax p ax = 0, which implies p = 10000 ax. = 10000 = 200. (c) let be the 90th percentile of l0. This means pr(l0 ) = 0. 9 pr((10000 + 200/0. 02)vtx 200/0. 02 ) = 0. 9. 20000 ) = 0. 9 pr(tx > 1 0. 02 ln( 10000+ . Since x = 0. 02 for all x, tx follows an exponential distribution with = 0. 02. This gives p = 238. 78: (a) from a2(cid:101) = 1 + v, we have v = 0. 8. (b) from (a), we have: 3 probability value of the present-value random variable, y.