- #1

IniquiTrance

- 190

- 0

## Homework Statement

5 people of ages (30M, 32M, 37F, 40M, 42F) enter into a life insurance contract where the one that outlives the others, receives a one time benefit of $1M, at the time of the penultimate death. What are the fair premiums (different), for each policy member?

## Homework Equations

## The Attempt at a Solution

In each iteration, I simulate the expected lifespans of each member, and focus on the one with the longest expected lifespan. I then discount the benefit back from the time of the penultimate death to each payment period, and make only the last to die, pay premiums.

After several million simulations, everyone has had their probabilistic opportunities to be the last to die, and I end up with respective premiums ($4458, $4705, $4679, $5180, $5088) +- $10.

Does this seem reasonable?

I think what this is essentially calculating is, say with person A:

[tex]\textbf{E}[\text{Person A's premium | A outlives everyone}]\bullet\textbf{P}[\text{A outlives everyone}][/tex]

Is this what I'm looking for?

I can't help questioning my assumption during each iteration, that only the longest living was paying the premiums. In the end, everyone is paying a premium.

This leads me to wonder whether it was necessary to use a copula function to create some kind of multivariate distribution...

Do I need to multiply these values by the probability of each outliving the others (I can keep track of how often each is in the lead)?

Thanks!

Last edited: