Link-save trading

Transaction costs involved while trading several assets may be described using bid-ask spread of the asset prices. We assume that the prices of several assets may be linked, so that transactions involving several assets have prices that are not necessarily equal to the sums of (bid or ask) prices of the individual assets. The family of possible price combinations forms a convex (random) set which changes in time and is called the set-valued price process. It is shown that the necessary and sufficient condition for no-arbitrage is the existence of a martingale selection, i.e. a martingale that takes values in the set-valued price process. Examples and applications to option pricing are discussed.