Modeling risk in a prescriptively plausible way represents a major issue in decision theory. The benchmarking procedure, being based on the satisficing principle and providing a probabilistic interpretation of expected utility (EU) theory, is prescriptive. Because it is a target-based language, the benchmarking procedure can be applied naturally to finance. In finance, the centrality of risk is widely recognized, but the risk measures that are commonly used to assess risk are too poor as a decision making tool. In this paper (...) we propose a two-stage decision criterion of choice under risk that provides an application of benchmarking to finance through a risk measure. We will analyze some nonexpected utility theories, in particular lottery dependent utility, as potential frameworks for our criterion. (shrink)