I am looking to collect stochastic optimization techniques to find a solution to the following problem
\begin{eqnarray*} &\text{maximize}\,\, \mathbb{E}(u(f(B)))\\ &\text{subject to }\,\,\, g_t(B)\geq 0, t\in[0,T] \end{eqnarray*} where $B$ is a random variable belonging to the nonnegative random variables, $f$ depends on $B$, $g$ is a function that depends on $t,B$ and $u$ is a convex function. I have read some results, but all of them cover cases where the constraint is static ($g(B)\geq0$ for instance), but not in this dynamic context. If someone knows of any results, such as papers or books that discuss this type of problem, I would appreciate it if you could provide me with that information. Thank you!.