Universal contingent claims and valuation multiplicative measures with examples and applications

We present and further develop the concept of a universal contingent claim introduced earlier by the author. This concept provides a unified framework for the analysis of a wide class of financial derivatives. Those, for example, include European, Bermudan and American contingent claims. We show that the value of a universal contingent claim is given by a multiplicative measure also introduced earlier by the author. Roughly speaking, a multiplicative measure is an operator-valued function on a semiring of sets which is multiplicative on the union of disjoint sets. We also show that the value of a universal contingent claim is determined by a, generally speaking, impulsive semilinear evolution equation also introduced earlier by the author.