Essential Supremum with Respect to a Random Partial Order
19 Pages Posted: 1 Apr 2013
Date Written: March 28, 2013
Abstract
Inspired by the theory of financial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in $\R^d$ is lifted to the space $L^0(\R^d)$ of $d$-dimensional random variables. In contrast to the classical definition, we define the essential supremum as a subset of random variables satisfying some natural properties. An application of the introduced notion to a hedging problem under transaction costs is given.
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