_ds.md

If $A$ and $B$ are sets then $A^B = {f\colon B\to A}$ is the set of functions from $B$ to $A$.

Exercise. The set $A^B$ has cardinality $a^b$ if $A$ has cardinality $a$ and $B$ has cardinality $b$.

One Period Model

Let $I$ be the set of instruments available for trading.

The prices at the beginning of the period are $x\in R^I$, $x(i)\in R$ is the initial price of instrument $i\in R$.

Let $\Omega$ be what can happen over the period.

The prices at the end of the period are $X\colon\Omega\to R^I$, $X(\omega)\in R^I$ are the prices if $\omega\in\Omega$ happened.