SOA's Other Sample M Problems

[Woody]

Along with the Societies infamous 157 Exam M problems, they also put out 11 problems dealing solely with Markov states (i.e. different states that can be represented by matrices). Has anyone done these problems and, if so, are they worth doing? I was going to start them last night, but with 2 weeks left, I want to use my time wisely and I wasn't sure if doing 11 of these problems is an efficient use of my time especially if there may be only 1 of these kind of problems on the exam. (Then again, the fact that they gave 11 of these kind to do may mean there might be 3 or 4 on the exam).

Also, the Society release 15 problems dealing with Asset Share and Incurances with expenses. These I do plan on doing, since I think they are easier to grasp than that Markov stuff.

[Maxprime]

Not trying to be annoying, but you should really do them all. You don't want 15 problems worth of material to bite you in the @ss. There's plenty of time, set aside an extra hour or two to crank these out - you'll be glad on Nov. 8th.

[MarsLasar]

They are easy to do and well worth it in my opinion.

[Brutè]

Are the eleven Markov problems the ones in the Jim Daniels note or is there another set of problems out there somewhere?

If it's the ones in the Daniels note, they are probably worth doing to get familiar with the new notation. Though I'm not sure that's necessary since the last exam didn't use the new notation in the Markov problems.

[MarsLasar]

No, and doing all the problems in the Daniel's note is a waste of time. But definitely do the special set of Markov probs the SOA put out.

[Woody]

All right, I'll do the Markov problems. I know that's the smart thing to do, I just am a little confused at how to approach them. I guess I got a little apprehensive when I couldn't understand the SOA's solution to the first problem. I had a hard time understanding what they were also saying in the problem itself.

Can someone explain in a simpler way how to tackle the first problem? I think if I understand how to do that one, the others should be pretty easy. I know they aren't that difficult, but I just can't seem to put my arms around these problems.

Thanks.

[Maxprime]

Originally Posted by Woody

All right, I'll do the Markov problems. I know that's the smart thing to do, I just am a little confused at how to approach them. I guess I got a little apprehensive when I couldn't understand the SOA's solution to the first problem. I had a hard time understanding what they were also saying in the problem itself.

Can someone explain in a simpler way how to tackle the first problem? I think if I understand how to do that one, the others should be pretty easy. I know they aren't that difficult, but I just can't seem to put my arms around these problems.

Thanks.

As a general rule, just write out a binomial (game theory) tree. At state 1, you can go to states 2 or 3 (whatever) and write probabilities along the way. Keep going as many times as they require and write the benefit at the bottom of the tree. To get expected value, just multiply the probabilities as you follow the tree down to the benefit - just add those up. As I always say, unless you are absolutely the world's most fluent matrix manipulator - you can only screw things up by avoiding this method. We don't have things like limiting probabilities anymore, so I can't think of a Markov problem where this approach wouldn't work. Just my .02.

[Woody]

Originally Posted by Maxprime

As a general rule, just write out a binomial (game theory) tree. At state 1, you can go to states 2 or 3 (whatever) and write probabilities along the way. Keep going as many times as they require and write the benefit at the bottom of the tree. To get expected value, just multiply the probabilities as you follow the tree down to the benefit - just add those up. As I always say, unless you are absolutely the world's most fluent matrix manipulator - you can only screw things up by avoiding this method. We don't have things like limiting probabilities anymore, so I can't think of a Markov problem where this approach wouldn't work. Just my .02.

That's good advice. I'll try it. I guess that whole kQn^(i,j) notation was confusing me. However, they give you a matrix to begin with. So how would you use a tree for problem 1?

Thanks.

[Maxprime]

Downloading/Printing the whole set right now - if I get it all printed out before lunch, I'll post up a response. If not, I'm sure someone will beat me to it.

[Maxprime]

You get your matrices for times 1 and 2 with probabilities (in the solutions if you need them).

Start out in state 1 (given)

From there you stay in 1 or go to 2, draw two lines down going to each.
Write on the sides of those lines the Probabilitiy you go to each (.73 & .26)

On your left leg should be state 1 (stayed in 1), you can stay in 1 again or go to 2, write down those probabilities from your year 3 matrix.

Do the same for the right side (starting in state 2 after coming from state 1).

Now, wherever you end up in state 1 is a path that will take you from state 1, forwards 2 years, ending up in state 1. Just multiply those probabilities down the legs to get the path you want and add them up.