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.