In modeling methods that require measurent of risk, uncertainty and certainty many researchers take into account two means of specifying parameters of terms of stochastic processes. One employs operators such at E( ), std( ) or skew( ). The other employs standard symbols for parameters, such as μ, σ or η1. The two approaches employ preceding superscripts differently. For example, the unconditional standard deviation of tX can be written as either std(tX) or tσ. Conditional on information available at time t – k, these become t–kstd(tX) and t|t–kσ. So, to give an even blunter example, tE( ) indicates a conditional expectation whereas tμ indicates an unconditional expectation. This unconditional expectation measures risk better when the model used captures the relevant factors for study.

You may want to have a look at the following papers. I think they would be helpful.

Conditional and dynamic convex risk measures

K Detlefsen, G Scandolo - Finance and Stochastics, 2005 - Springer.

Risky debt, mixed-attribute accounting, and the identification of conditional conservatism

WH Beaver, SG Ryan - 2009 - papers.ssrn.com