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Abstract

In this chapter we review the theory of dynamic programming in continuous time. This can be done within the framework of a general controlled Markov process, but in order to keep the theory reasonably concrete we restrict ourselves to the case of a controlled stochastic differential equation (SDE) driven by a finite-dimensional Wiener process. The extension to an arbitrary controlled Markov process is rather obvious and we will comment upon it later. As the reader will see, the arguments in the continuous-time case will be almost exactly the same as for the discrete-time case.

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References

  • Fleming, W., & Rishel, R. (1975). Deterministic and stochastic optimal control. Springer.

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  • Krylov, R. (1980). Controlled diffusion processes. Springer.

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  • Øksendal, B. (2013). Stochastic differential equations: An introduction with applications (5th ed.). Springer.

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Björk, T., Khapko, M., Murgoci, A. (2021). Dynamic Programming Theory. In: Time-Inconsistent Control Theory with Finance Applications. Springer Finance. Springer, Cham. https://doi.org/10.1007/978-3-030-81843-2_11

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