Abstract: A first price and first size of a published offer to sell shares of a security are determined, and a second price and second size of orders to sell shares of the security are determined. A third price and third size of orders to sell shares of the security are determined, wherein the second price is greater than the published offer and the third price is greater than the second price. A market order to buy shares of the security is received with a buy size greater than a sum of the first size and the second size. A first portion of the market order that is equal to the first size is executed at a first price, and a second portion of the market order is executed at the third price. The sum of the size of the first portion and the size of the second portion equals the buy size. Market orders to sell are handled in a similar fashion.

Abstract: A buy order is received with a limit price that is above a published best offer, and represented in the auction market. If the buy order is not immediately executed, it is quoted at a minimum variation better than a published best bid, and the price of the quoted buy order becomes the published best bid. Alternatively, a sell order is received with a limit price that is below a published best bid, and represented in the auction market. If the sell order is not immediately executed, it is quoted at a minimum variation better than a published best offer, and the price of the quoted sell order becomes the published best offer.

Abstract: An exchange through which one or more trades of a security were executed issues an advertisement indicating the security, the amount traded over a given period, the trader and other pertinent information along with an indication that these trades were executed in the exchange. This enables the recipient of these advertisements to receive for the first time added confidence of trading capability in a given security.

Abstract: A method and apparatus optimizes tax treatment of business transactions by determining in advance the taxes that would be due in each of several possible jurisdictions. Once the tax results are presented to the user, the user can select in which jurisdiction to execute the transaction. Once the jurisdiction is selected, information regarding execution of the transaction is forwarded to a computer located in the selected jurisdiction and the transaction is then executed in the computer in the selected jurisdiction. The method and apparatus help conduct business transactions electronically over an internationally operated distributed computer network, such as the Internet, and execute the transaction in a jurisdiction selected to minimize the taxes while transferring the money and assets, rights or liabilities from the parties in jurisdictions in which the money and assets, rights or liabilities are located.