Week 4 lecture.pdf

Week 4 lecture.pdf - ETC2430 Actuarial Statistics Lecture...

  • No School
  • AA 1
  • 20

This preview shows page 1 - 4 out of 20 pages.

1 ETC2430 Actuarial Statistics Lecture Notes Week 4 Valuing Cashflows 1. Valuing cashflows Consider times t 1 and t 2 , where t 2 is greater than t 1 . Since t 1 < t 2 , the discounted value at time t 1 of C due at time t 2 is: 𝐶?𝑥𝑝 [− ∫ 𝛿(?)?? ? 2 ? 1 ] Since: 𝛿(?)?? ? 2 ? 1 = ∫ 𝛿(?)?? ? 2 0 − ∫ 𝛿(?)?? ? 1 0 And given that 𝑣(?) = ?𝑥𝑝 (− ∫ 𝛿(?)?? ? 0 ) it follows that the value at time t 1 of C due at time t 2 is: 𝐶 𝑣(? 2 ) 𝑣(? 1 ) This tells us that in order to find the value at time t 1 of C due at time t 2 , we can discount both amounts back to time 0, and then calculate the difference. Question: Calculate the value at time 4 of a payment of 860 at time 10 if 𝑣(10) = 0.76 and 𝑣(4) = 0.91 . Solution: The value at time 4 is: 860 × 𝑣(10) 𝑣(4) = 860 × 0.76 0.91 = 718.24
Image of page 1

Subscribe to view the full document.