  We give an axiomatic framework for conditional generalized deviation
measures. Under financially reasonable assumptions, we give the correspondence
between conditional coherent risk measures and generalized deviation measures.
Moreover, we establish the notion of continuous-time risk contribution for
conditional coherent risk measures and generalized deviation measures. With the
help of the correspondence between these two different types of risk measures,
we give a microscopic interpretation of their risk contributions. Particularly,
we show that the risk contributions of time-consistent risk measures are still
time-consistent. We also demonstrate that the second element of the BSDE
solution $(Y, Z)$ associated with $g$-expectation has the meaning of risk
contribution.
