Continuous Insurances with Constant Forces of Mortality (Part One)

You know those great, simplified formulas you get to use for continuous insurances when the force of mortality is constant? Here I derive them from first principles. The goal is to understand where these formulas come from - that way if we blank on the exam, we can quickly reproduce them.

In the first three and a half minutes, I explain why we integrate what we do to get the actuarial present value of a continuous whole life insurance. Derivations of the simplified formulas for each insurance can be found at the following times:
Whole life - 3:48; Term - 5:32; Pure Endowment - 7:55; Deferred - 9:14
Joint status is discussed in part two of this video.

Category:

Education

Tags:

• insurance
• constant force of mortality
• constant mortality
• term
• pure
• endowment
• deferred
• soa
• mlc
• life contingencies

[mlctutor]

You are absolutely right, good catch. I will post a correction in the next few days. Thank you!

[Pyretix]

I can't believe these vids have so few views. Enjoy your first like, just as I enjoyed my A on my homework :-D

[45cmdr]

Just a small note on the discrete whole life example (@2:19), your probabilities of death are written down as qx, 1|qx+1, 2|qx+2. I believe they should read: qx, 1|qx, 2|qx as you want to express deferred probabilities based on the same starting age. You could also write them down as: qx, px*qx+1, px*px+1*qx+2