What are some good references to study Stochastic Control with applications to Finance, like the Merton problem and other variants? Books or review papers?
Peter Forsyth of UWaterloo is my favourite author on this topic (one of my top three in MathFin!)
Optimal allocation under wealth goals, optimal decumulation strategies, etc
I find his writing style very honest and open, yet to find a typo and the notation is super clear.
it is a bit late but the 2007 book "Applied Stochastic Control of Jump Diffusions" from Oksendal and Sulem is quite good too.