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Math Help - Perfect information

  1. #1
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    Perfect information

    Not sure if this is a basic pre uni question but since I'm covering it at uni I will assume that it fits under the advanced section.

    I'm trying to solve a question that asks me to suggest the best investment choice given a payoff table. In the table I am given 4 investments, one of which returns the same amount in all cases, and the other three vary. The question then goes on to say that assuming that the return on one of the remaining three investment classes will be known... which of the four would be the best choice.

    The problem that I'm having is figuring out how to calculate the expected profit under perfect information. The definitions that I've seen regarding this are very clear... i.e. it is the sum of the expected profit under uncertainty (easy) and the amount a decision maker is willing to pay to gain perfect information.

    To me, the expected profit of perfect information is just the outcome that you predict. i.e. out of lets say 3 possible outcomes, loss, break even and gain (theres 5 in the question but doesn't matter) lets say we know that a gain will take place. Therefore this becomes the expected profit. Question is... if I'm not told which outcome will occur, how do I compare the 4 asset classes and decide the best one?

    I found this

    http://www.answers.com/topic/decision-theory

    as an example showing how to calculate perfect information, but I didn't understand it as it was rather poorly annotated.

    Is this even a mathematical question? I was thinking of answering it along the lines of risk profiles (risk taking, risk neutrality and risk aversion) but I can't help but feel that this is wrong.

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Atomic_Sheep View Post
    Not sure if this is a basic pre uni question but since I'm covering it at uni I will assume that it fits under the advanced section.

    I'm trying to solve a question that asks me to suggest the best investment choice given a payoff table. In the table I am given 4 investments, one of which returns the same amount in all cases, and the other three vary. The question then goes on to say that assuming that the return on one of the remaining three investment classes will be known... which of the four would be the best choice.

    The problem that I'm having is figuring out how to calculate the expected profit under perfect information. The definitions that I've seen regarding this are very clear... i.e. it is the sum of the expected profit under uncertainty (easy) and the amount a decision maker is willing to pay to gain perfect information.

    To me, the expected profit of perfect information is just the outcome that you predict. i.e. out of lets say 3 possible outcomes, loss, break even and gain (theres 5 in the question but doesn't matter) lets say we know that a gain will take place. Therefore this becomes the expected profit. Question is... if I'm not told which outcome will occur, how do I compare the 4 asset classes and decide the best one?

    I found this

    Decision theory: Definition from Answers.com

    as an example showing how to calculate perfect information, but I didn't understand it as it was rather poorly annotated.

    Is this even a mathematical question? I was thinking of answering it along the lines of risk profiles (risk taking, risk neutrality and risk aversion) but I can't help but feel that this is wrong.

    Thanks
    If you know the return, then the expected return is that return (since it occurs with probability 1, and all other alternatives (and combinations of alternatives) occur with probability 0)

    CB
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  3. #3
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    Yep, I understand that, but as I said, I'm not told which of the 3 outcomes will occur. Lets say I was told that my outcome for that asset class (for which I have perfect knowledge) will be profit with the one that generates the same returns in all states giving me losses of the same size and the remaining 2 giving me break even. In that case it's a pretty simple decision. The problem is that not only am I not given the probabilities of the outcomes to the other two (not perfect knowledge) asset classes which makes the calculation of their respective expected profits impossible, but I'm not given what outcome will take place for the one perfect knowledge asset class. Therefore it is impossible to asses which of the 4 is the best option.

    My greatest concern is the fact that I'm given the payoff table, so I can't imagine it not needing to be used to answer the question. There are other parts to the question that state the probabilities but they are in a completely different part and I'm almost 100% certain that those probabilities can't used to answer this part that I'm talking about. The more I read the question, the more I believe it's a very theoretical type question but I'm just not sure.

    EDIT: I now understand how to answer the question. I believe that has to be done is a discussion has to be carried out, analysing the outcomes one by one under the assumption that that is the outcome that has taken place. So simple .
    Last edited by Atomic_Sheep; October 27th 2009 at 06:05 AM.
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