Abstract: An apparatus for processing trading orders, comprising: a central server connectable to a plurality of terminals on which user orders are to be entered.

Abstract: An optimization method comprises specifying an event; defining a set of outcomes for said event; defining at least one function representing a transaction between an exchange and another party, said at least one function being dependent on the outcome of said event; receiving, at said exchange, orders for at least one said transaction from at least one other party; constructing a map between the space defined by said at least one function and the space defining the proportion to which each received order is to be accepted; defining a hedging condition representing the maximum risk to which the exchange is to be exposed, using said map; defining at least one optimization criterion; calculating a solution for the values of the coefficients representing the proportions of each order to be accepted, subject to said hedging condition and said optimization criterion.

Abstract: A system which can easily and cheaply be installed to an existing rail infrastructure is disclosed which seeks to avoid the likelihood of train collisions. Each train travelling on a network is provided with a means for determining its own position (such as a GPS receiver) and a means for communicating with a central controller. The train's position is communicated to the central controller and the central controller uses this information to work out where each train is located on the network. Velocity and acceleration information are obtained by monitoring the train's position over time and predictions are made as to the future position of each of the trains on the network. If the future position of any of the trains is determined to be in a range which at least partially overlaps a range of future positions for another train then a collision warning is sent to one or both trains. This warning could trigger the train to stop automatically or for the driver to apply the breaks.