In financial mathematics, a conditional risk measure is a random variable of the financial risk (particularly the downside risk) as if measured at some point in the future. A risk measure can be thought of as a conditional risk measure on the trivial sigma algebra. 
A dynamic risk measure is a risk measure that deals with the question of how evaluations of risk at different times are related. It can be interpreted as a sequence of conditional risk measures. 
A different approach to dynamic risk measurement has been suggested by Novak.
Conditional risk measure.
Consider a portfolio's returns at some terminal time formula_1 as a random variable that is uniformly bounded, i.e., formula_2 denotes the payoff of a portfolio. A mapping formula_3 is a conditional risk measure if it has the following properties for random portfolio returns formula_4:
 formula_5
 formula_6
 formula_7
If it is a conditional convex risk measure then it will also have the property:
 formula_8
A conditional coherent risk measure is a conditional convex risk measure that additionally satisfies:
 formula_9
Acceptance set.
The acceptance set at time formula_10 associated with a conditional risk measure is
 formula_11.
If you are given an acceptance set at time formula_10 then the corresponding conditional risk measure is
 formula_13
where formula_14 is the essential infimum.
Regular property.
A conditional risk measure formula_15 is said to be "regular" if for any formula_16 and formula_17 then formula_18 where formula_19 is the indicator function on formula_20. Any normalized conditional convex risk measure is regular.
The financial interpretation of this states that the conditional risk at some future node (i.e. formula_21) only depends on the possible states from that node. In a binomial model this would be akin to calculating the risk on the subtree branching off from the point in question.
Time consistent property.
A dynamic risk measure is time consistent if and only if formula_22.
Example: dynamic superhedging price.
The dynamic superhedging price involves conditional risk measures of the form 
formula_23. 
It is shown that this is a time consistent risk measure.
References.
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