  We present new formulations of the stochastic electricity market clearing
problem based on the principles of stochastic programming. Previous analyses
have established that the canonical stochastic programming model effectively
captures the relationship between the day-ahead and real-time dispatch and
prices. The resulting quantities exhibit desirable guarantees of revenue
adequacy, cost recovery, and price distortion in expectation. Motivated by
these results, we develop alternative stochastic programming model formulations
that differ in how we model the nonanticipativity requirement. We design new
pricing mechanisms by developing suitable dual optimization problems for these
models. We analyze these pricing mechanisms to assess their ability to provide
revenue adequacy for the system operators, cost recovery for generators, and
price distortion. Unlike the previous mechanisms that yield the desired
properties in expectation, one of our pricing mechanisms extends the benefits
of cost recovery and bounded price distortion under every scenario while
retaining the long-run revenue adequacy for the system operator. We demonstrate
these benefits through numerical experiments conducted on well-known test
systems.
