Scalar Multivariate Risk Measures with a Single Eligible Asset

In this paper, we present results on scalar risk measures in markets with transaction costs. Such are defined as the minimal capital requirements cash asset. First, some provided dual representation of such measures, particular emphasis given space variables (equivalent) martingale and prices consistent market model. Then, these representations used to obtain main paper time consistency for frictions. It is well known from superhedging measure costs that usual concept too strong not satisfied. We will show a weaker notion can be defined, which corresponds but under any fixed pricing process. prove equivalence certain type backward recursion respect underlying Several examples given, special measure.