The risk of a financial position shines through by means of the fluctuation
of its market price. The factors affecting the price of a financial position
include not only market internal factors, but also other various market
external factors. The latter can be understood as sorts of environments to
which financial positions have to expose. Motivated by this observation, this
paper aims to design a novel axiomatic approach to risk measures in random
environments. We construct a new distortion-type risk measure, which can
appropriately evaluate the risk of financial positions in the presence of
environments. After having studied its fundamental properties, we also
axiomatically characterize it. Furthermore, its coherence and dual
representation are investigated. The new class of risk measures in random
environments is large enough, for example, it not only can recover some known
risk measures such as the common weighted value at risk and range value at
risk, but also can induce other new specific risk measures such as risk
measures in the presence of background risk. Examples are given to illustrate
the new framework of risk measures. This paper gives some theoretical results
about risk measures in random environments, helping one to have an insight look
at the potential impact of environments on risk measures of positions.Comment: 47 pages, no figure