Optimal Control with Noisy Time

Andrew Lamperski; Noah J. Cowan

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arXiv · 1401.0202

Optimal Control with Noisy Time

Andrew Lamperski·Noah J. Cowan

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Abstract

This paper examines stochastic optimal control problems in which the state is perfectly known, but the controller's measure of time is a stochastic process derived from a strictly increasing L\'evy process. We provide dynamic programming results for continuous-time finite-horizon control and specialize these results to solve a noisy-time variant of the linear quadratic regulator problem and a portfolio optimization problem with random trade activity rates. For the linear quadratic case, the optimal controller is linear and can be computed from a generalization of the classical Riccati differential equation.

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BibTeX RIS

Andrew Lamperski, Noah J. Cowan. 2013-12-31. Optimal Control with Noisy Time. https://arxiv.org/abs/1401.0202

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