[SOLVED] ACTU PS5821 Actuarial Methods – Autumn 2024 Assignment – 2 Matlab

ACTU PS5821 Actuarial Methods – Autumn 2024

Assignment – 2

Assigned 9/13/24, Due 9/21/24

Problem 1. Mortality follows the following survival function

S0(x) = 0.1√100 − x, 0 ≤ x ≤ 100 = limiting age

Calculate that a new born dies between ages 19 and 36.

Problem 2. Mortality follows

F0(x) = 1 − 1 + x/1

Calculate

(a) p20

(b) 10|5q30

Problem 3. Mortality follows µx+t = 0.002 + 0.001t for 0 ≤ t ≤ 1. Calculate qx.

Problem 4. Consider a life currently aged x, let T be the time lived by (x) after the age of x + n. Find the distribution of T

Problem 5. A new machine component is assumed to fail at time T, where the force of failure is

µt = 4(10 − t)/1, for 0 ≤ t < 10

Derive the density function and the survival function for this distribution