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

1. ## 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.

2. ## 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.

3. ## 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?

4. ## 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.