Home Forums Actuarial Resources & Blogs Life Contingencies School Level Maths Proof 2

Viewing 1 post (of 1 total)
  • Author
    Posts
  • #23556
    Richard Purvey
    Participant

      Life Contingencies School Level Maths Proof 2

      Starting with the two equations:
      <p style=”text-align: center;”>1. e^(-delta)=v and</p>
      2. (1-d(m)/m)^m=v, show that lim m→infinity d(m)=delta.

      Method

      Re-arranging equation 1. gives delta=-ln(v) and re-arranging equation 2. gives d(m)=m*(1-v^(1/m)), meaning that lim m→infinity d(m)=lim m→infinity m*(1-v^(1/m)), which, after using an Online Limits Calculator, is found to equal –ln(v) which equals delta.

    Viewing 1 post (of 1 total)
    • You must be logged in to reply to this topic.