Results 1 to 4 of 4

Math Help - Interpretation null and power set in filtration for a multi period model

  1. #1
    Newbie
    Joined
    May 2013
    From
    Nederland
    Posts
    5

    Interpretation null and power set in filtration for a multi period model

    Hi there,

    I'm wondering about the actual interpreation of the null and power set in a filtration on a probability space for a binomial model.

    For a two period model the information set at time 0 F_{0} = \{\Omega, \emptyset\}.
    For a two period model the information set at time 1 F_{1} = \{\Omega, \emptyset, \{uu,ud\}, \{du, dd\}\}.
    For a two period model the information set at time 2 F_{2} = 2^\Omega.

    As far as I understand.
    Now at time 1 it seems logical that you know whether u or d has occurred so you know at that time that you will end up with either uu or ud if u has occurred or du or dd if d has occurred.
    But I find it hard to interpret the empty and power set at this time. What extra information does this represent? Could someone push me in the right direction here?

    Kind regards Mkkl.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Interpretation null and power set in filtration for a multi period model

    Hey Mkkl.

    One way that may help is that the universal set refers to any probable event while the null refers to no event within the event space. So A null event corresponds to nothing happening and a universal set represents to any valid event (no matter if its an atomic one, conditional one, or whatever) happening.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2013
    From
    Nederland
    Posts
    5

    Re: Interpretation null and power set in filtration for a multi period model

    So since the first u or d has already occurred, should I interpret the null and power set as something happening other than a second up or down event? Whatever that may be?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Interpretation null and power set in filtration for a multi period model

    The universal event means that something that is possible, has happened.

    The way I would interpret the null set is in terms of having no information whatsoever: so like an empty sample with no observations.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 11th 2012, 01:52 AM
  2. Replies: 1
    Last Post: September 11th 2012, 01:51 AM
  3. Replies: 0
    Last Post: March 15th 2012, 01:04 PM
  4. The interpretation of the null-space
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 10th 2012, 09:31 AM
  5. Spring Model Interpretation!
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: November 2nd 2008, 07:07 AM

Search Tags


/mathhelpforum @mathhelpforum