  The family of admissible positions in a transaction costs model is a random
closed set, which is convex in case of proportional transaction costs. However,
the convexity fails, e.g. in case of fixed transaction costs or when only a
finite number of transfers are possible. The paper presents an approach to
measure risks of such positions based on the idea of considering all selections
of the portfolio and checking if one of them is acceptable. Properties and
basic examples of risk measures of non-convex portfolios are presented.
