References to learn continuous-time dynamic programming Does anyone know of good references to learn continuous-time dynamic programming? The references don't have to be books. They could be links to online resources as well. Links to clear, concise discussions of even just the basics would be helpful.
For continuous-time stochastic dynamic programming, the small, nontechnical Art of Smooth Pasting by Dixit is a wonderful option. It does a very effective job of conveying the basic intuition.

Stokey's more recent The Economics of Inaction is also decent, but for a practical-minded person it probably underperforms Dixit - its much greater length and somewhat heavier notation do not yield commensurate rewards.



If the underlying stochastic processes are not Itō diffusions, then I'm not sure what the best reference is. The most common such case I've seen (and that I use myself) is the case of discretely many exogenous states, where if we are currently in state $s$ there is some constant hazard rate $\lambda_{s,s'}$ of a switch to state $s'$. Fortunately, this is a pretty simple case in practice: one can just modify the HJB equation to account for the flow probability of switching from $V(\cdot,s)$ to $V(\cdot,s')$. (You can see this, for instance, in equations (1)-(5) in this Acemoglu and Akcigit paper. Conceptually it's no different from setting up the HJB equation when we have an Itō diffusion as the driving process, except that it's simpler because we just get a system of linear equations and we don't need to think about Itō's lemma, etc.)

Of course, maybe there is a good textbook reference for this too - but unlike the potentially much more complicated cases involving stochastic calculus, this is straightforward enough that a text has never seemed necessary to me.