Spring 2011 Discussion

[Wolf Follower]

Think I got 2-something for the gambling one. I used the BErnoulli shortcut for variance.

I also got 0.5 for the last one - the order statistics one. I wrote out and integrated the pdf just to make sure.

The Markov chain one where we had to find P, did everyone interpret that as receiving the last payment at time 4, making the incoming and outgoing offset by 1?

WF

[MrTomD]

Originally Posted by Theophilus

I got .5 for the last one as well. 208 for the gambling one I think....

So did I. Last question = 0.5

[Is This Wilt Chamberlain?]

I always draw Binomial Trees for those Markov ones (thanks MFE), I find it helps keep everything straight. I don't remember my answer though.

[Theophilus]

The two I could not answer were the multi-decrement problem and the lifecon problem with given values for two different premiums and a reserve that asked you to solve for a third premium.

[Is This Wilt Chamberlain?]

Originally Posted by Wolf Follower

The Markov chain one where we had to find P, did everyone interpret that as receiving the last payment at time 4, making the incoming and outgoing offset by 1?

WF

Hmm, pretty sure I started P at time 1 (so v1, v2, v3). I think it said P happened at the beginning of the year when it switched from state 2 to state 1 (or whichever it was)..so I assumed that the switch from year 0 to year 1 counted. I hope I didn't do that one wrong, I was sure that was a +2.

[peem]

I recall being quite a bit below the 0.95th percentile of the Chi-square distribution for the Chi-square problem...

For some reason, I was struggling with the prob exactly one death problem... I had to end of guessing on that one...

For one of the Poisson problems, time til the 2nd event... I believe I found lambda' = (lambda)S(30K). Then Time til the 2nd event is Gamma(alpha=2, theta = 1/lambda'). Var = (theta)(1/lambda')^2.

Sorry. Too lazy to Tex.

The very first question I believe was a gimme, unless I totally screwed that one up. (1/mu)^2

[dballs33]

Will a PAK be started?

[MrTomD]

Originally Posted by Theophilus

The two I could not answer were the multi-decrement problem and the lifecon problem with given values for two different premiums and a reserve that asked you to solve for a third premium.

I believe there was a simple formula to find the other P when given the other two P's and the reserve. (Thanks MLC)

[Is This Wilt Chamberlain?]

Originally Posted by peem

The very first question I believe was a gimme, unless I totally screwed that one up. (1/mu)^2

Yeah that was nice of them. I still spent a minute staring at it saying "I have to be missing something..."

[Wolf Follower]

Originally Posted by Is This Wilt Chamberlain?

Hmm, pretty sure I started P at time 1 (so v1, v2, v3). I think it said P happened at the beginning of the year when it switched from state 2 to state 1 (or whichever it was)..so I assumed that the switch from year 0 to year 1 counted. I hope I didn't do that one wrong, I was sure that was a +2.

I wouldn't worry about it. I may well be wrong. Interpreting the times is usually the biggest challenge in Markov Chain problems.

WF