Discretisation of stochastic control problems for continuous time dynamics with delay
Markus Fischer,Markus Reií +1 more
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In this article, the existence of an optimal strategy with respect to the cost functional can be guaranteed in the class of relaxed controls in continuous-time control problems in continuous time, where the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2007-08-20 and is currently open access. It has received 10 citations till now. The article focuses on the topics: Markov process & Markov chain.read more
Citations
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Journal ArticleDOI
A stochastic control problem with delay arising in a pension fund model
TL;DR: The equivalence between the one-dimensional delay problem and the associated infinite-dimensional problem without delay is shown and it is proved that the value function is continuous in this infinite- dimensional setting.
Journal ArticleDOI
Finite-Dimensional Representations for Controlled Diffusions with Delay
Salvatore Federico,Peter Tankov +1 more
TL;DR: In this article, the authors studied stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process and provided sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation.
Journal ArticleDOI
Time Discretisation and Rate of Convergence for the Optimal Control of Continuous-Time Stochastic Systems with Delay
Markus Fischer,Giovanna Nappo +1 more
TL;DR: In this article, a semi-discretisation scheme for stochastic optimal control problems whose dynamics are given by controlled stochiastic delay (or functional) differential equations with bounded memory is studied.
Posted Content
Finite-dimensional representations for controlled diffusions with delay
Salvatore Federico,Peter Tankov +1 more
TL;DR: In this article, the authors study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process and provide sufficient conditions under which a linear path functional of the solution of a SDDE admits a finite-dimensional Markovian representation.
Journal ArticleDOI
Recurrent neural networks for stochastic control problems with delay
Jiequn Han,Ruimeng Hu +1 more
TL;DR: In this paper, the authors employ neural networks for sequence modeling (e.g., recurrent neural networks such as long short-term memory) to parameterize the policy and optimize the objective function.
References
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Numerical solutions of stochastic functional differential equations
TL;DR: In this paper, the strong mean square convergence theory is established for the numerical solutions of stochastic functional differential equations (SFDEs) under the local Lipschitz condition and the linear growth condition.
Journal ArticleDOI
Dynamic programming in stochastic control of systems with delay
TL;DR: In this article, the authors consider optimal control problems for systems described by stochastic differential equations with delay (SDDE) and prove a version of the dynamic programming principle for a general class of such problems.
Journal ArticleDOI
Projection Pursuit for Exploratory Supervised Classification
TL;DR: New indices derived from linear discriminant analysis that can be used for exploratory supervised classification are introduced.
Journal ArticleDOI
Numerical approximations for nonlinear stochastic systems with delays
TL;DR: The Markov chain approximation method for nonlinear delayed reflected diffusion models was introduced by Kushner, H.J. and Dupuis, P. as discussed by the authors, which is robust, the approximation has physical interpretations as control problems closely related to the original one, and there are many effective methods for getting the approximations, and for solving the Bellman equation for low-dimensional problems.
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