Dynamic risk measure
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  as a random variable that is uniformly bounded, i.e.,  denotes the payoff of a portfolio.  A mapping  is a conditional risk measure if it has the following properties for random portfolio returns :

 Conditional cash invariance
 

 Monotonicity
 

 Normalization
 

If it is a conditional convex risk measure then it will also have the property:

 Conditional convexity
 

A conditional coherent risk measure is a conditional convex risk measure that additionally satisfies:

 Conditional positive homogeneity

Acceptance set

The acceptance set at time  associated with a conditional risk measure is
 .

If you are given an acceptance set at time  then the corresponding conditional risk measure is
 
where  is the essential infimum.

Regular property
A conditional risk measure  is said to be regular if for any  and  then  where  is the indicator function on .  Any normalized conditional convex risk measure is regular.

The financial interpretation of this states that the conditional risk at some future node (i.e. ) 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 .

Example: dynamic superhedging price
The dynamic superhedging price involves conditional risk measures of the form 
.  
It is shown that this is a time consistent risk measure.

References

Financial risk modeling