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I have an optimal stopping and control problem for which the dynamic programming equation is written. I am totally new to this field and type of problem but I have bases in Stochastic Calculus and Stats. I just don`t understand where to start to solve this stuff.

TLDR: I need help getting started with Viscosity Solution to Stochastic Control Problem.

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  • $\begingroup$ Dynamic Programming is a huge field, with many exact and approximate techniques for various cases. It would help matters considerably if you provide the details of your problem and where you need help. In Dynamic Programming, It's often much easier to write the Bellman Equation for a particular problem and state space than it is to solve it. Not all state space definitions and corresponding Bellman Equations for the same problem are of equal difficulty to solve. $\endgroup$ – Mark L. Stone Jun 19 '15 at 19:17
  • $\begingroup$ Here are a couple of "random" Google hits (I am not vouching for their correctness, goodness, or applicability to your problem, which I have no idea what it is). cmap.polytechnique.fr/~touzi/pise02.pdf icts.res.in/media/uploads/Program/Files/Suresh.pdf . $\endgroup$ – Mark L. Stone Jun 19 '15 at 19:25
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For a gentle introduction,may I suggest "Reinforcement Learning: An Introduction" . It concentrates on discrete rather than continuous problems but gives a nice overview of stochastic control problems.

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  • $\begingroup$ great read, baby steps and big picture. Just the way I like it. $\endgroup$ – not.so.quanty Jun 22 '15 at 15:30
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Custom-made for you: Dynamic Programming and Optimal Control. The author, Dimitri P. Bertsekas, is a leader in the field of dynamic programming. I don't know if it is the right approach for your problem, though; I am only addressing the titular question.

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