On the law of one price
The authors study the law of one price (L1P) that is weaker than no arbitrage (NA) property of financial market. It can be formulated for one-period model as follows: the identity \(x+h\xi=x'+h'\xi\), where \(h,h'\in \mathbf R^d\), implies that \(x=x'\) (here \(\xi\in\mathbf R^d\) is a random vector describing price increments). In other words, if a contingent claim has a price, namely, a replication price, this price is unique. Clearly, this property is always fulfilled if NA holds. The aim of the paper is to analyze the law of one price for the multi-period model with a general probability space. The main result is that the law of one price holds if and only if there exists a martingale density process with strictly positive initial value. In contrast to the classical no-arbitrage criteria, this density process may change its sign. It is also shown that under such a weak condition as L1P the market portfolio exists.
scientific article; zbMATH DE number 2169547