Time Discretisation and Rate of Convergence for the Optimal Control of Continuous-Time Stochastic Systems with Delay |
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Authors: | Markus Fischer Giovanna Nappo |
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Institution: | (1) Institute for Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany;(2) Department of Mathematics, University of Rome “La Sapienza”, Piazzale Aldo Moro 2, 00185 Rome, Italy |
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Abstract: | We study a semi-discretisation scheme for stochastic optimal control problems whose dynamics are given by controlled stochastic
delay (or functional) differential equations with bounded memory. Performance is measured in terms of expected costs. By discretising
time in two steps, we construct a sequence of approximating finite-dimensional Markovian optimal control problems in discrete
time. The corresponding value functions converge to the value function of the original problem, and we derive an upper bound
on the discretisation error or, equivalently, a worst-case estimate for the rate of convergence. |
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Keywords: | Optimal control Stochastic differential equation Functional differential equation Delay Time lag Finite differences Time discretisation Approximation Error bound Convergence rate |
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