Expected Return Question

Discussion in 'Risk Management' started by dima777, Oct 3, 2008.

  1. dima777


    I am wondering what is the expected return on earning an infinite sum of money which has an almost zero chance of occurrence - probability of, say, one in a trillion (but NOT zero). Will the expected return be still infinite?
  2. MGJ


    Dig out your Introduction To Calculus book and reacquaint yourself with L^Hopital's Rule and other "limit as x approaches infinity" products and quotients.
  3. ronblack


    E = p x W - (1-p)L

    where: p = probability of win ~ 0
    W = infinity
    L = 0

    plug in and you get: E = p x W

    If p is small but still finite , then E = infinity. As p goes to zero in the limit, E becomes an undefined quantity.

    This means it can be either 0 or infinity, as already assumed, or any other value in between depending on many other factors.

    The question is: when does E start becoming an undefined quantity?

    This is related to St Petersburg paradox. The paradox arises because of the use of infinity in a decision process.

    No natural decision process can involve infinity since the universe itself is not infinite.

    Drop infinity and you are ok. In this game your ticket will cost a lot of money.
  4. dima777


    thanks..but i do not understand why you think p the should go down to zero....it is a fairy small number but it is a fixed one..and infinity is also a "fixed" value - there is no need to approach it though a limit...
  5. The simple question you should ask yourself is this -- is a fraction of infinity less than infinity?

    <i> That is whole, this is whole
    From the whole, the whole is subtracted
    When the whole is taken from the whole
    The whole still will remain —
    --Upanishad. </i>