**1. Introduction**__Definition__: the simultaneous buying and selling of securities, currency, or commodities in different markets or in derivative forms in order to take advantage of differing prices for the same asset.**2. Option Pricing**

**Question:**

__How to choose x and y:__

__How to maximize profit:__

__Key Assumption:__ There is no limit to buying or selling of options. In practice,

you may only be able to buy, but no sell, for example.**3. Aibitrage Theorem**__Definition:__

Consider n possible wagers on m possible outcomes: .

Let to be the outcome of wagers i if outcome j occurs.

If is bet on wager , then is earned if outcome j occurs.**Arbitrage Theorem:**

- such that ,
- such that

Intuitively,

- First theorem: there is a probability vector such that the expected outcome of every bet is 0, or
- There existing a betting scheme that leads to a sure win.

## TODO: explain more about these two theorem