KEY POINTS

• A complete market is one in which any desired future payoff can be generated by a suitable portfolio of the existing assets in the economy.
• In a world where the number of states (future scenarios) is finite, a market is complete if and only if this number is equal to the rank of the asset payoff matrix. In particular, it is necessary for the number of assets be greater than the number of states.
• The Law of One Price states that any two assets with identical payoffs in the future must have the same price today.
• A linear pricing rule means that the price of a basket of assets is equal to the sum of the prices of those assets in the basket. The Law of One Price is true if and only if the linear pricing rule is true.
• The state price is the price one has to pay today to obtain a one dollar payoff in a particular future state and nothing in other states. The existence of the state price is equivalent to the validity of the Law of One Price. It will be unique if the market is complete.