What is a good book for MDP with a stress on solving them using DP? However, the book should stress on the theorems and proofs and make a case for why DP is the most popular tool to solve MDPs.
I am not looking for an introductory book but a book that can stress on the maths behind MDP and why DP is used to solve it mostly?
Algorithms are not necessarily required in the book. If the book also addresses the question of developing algorithms that's a bonus.
One desired requirement is that the book be concise and to the point. It should try to be within 200 pages but still cover all the core technical details.
I am in interested in learning to write proofs for certain stochastic MDP results that i am working with.
This is not a whole book, but I recommend the chapter on controlled Markov chains in Kushner, Harold, and Paul G. Dupuis. Numerical methods for stochastic control problems in continuous time. Vol. 24. Springer Science & Business Media, 2013.
Another option is Puterman, Martin L. Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons, 2014, though I have not read it myself.