There are a variety of control problems for controlled diffusions $X_t^u$, with the terminal cost given by $$ J(u)\triangleq \mathbb{E}\left[g(X_T,u)+\int_0^t h(X_t,u_t)ds\right], $$ function $g$ and running cost $h$ are Lipchutz (and nice). Is there any literature on stochastic optimal control problems where the cost is given by $$ \tilde{J}(u)\triangleq G(X_T,u) + \mathbb{E}\left[\int_0^t h(X_t,u_t)ds\right], $$ where $G$ is a convex functional from $L^1(\mathcal{F}_T)\rightarrow \mathbb{R}$?
I'm looking for references and/or the name of this type of control problem. Thanks.

Note: (Of course the cost functionals of the form $\tilde{J}$ generalize those of the form $J$).


Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.