We are concerned with stochastic control systems composed of a large number of N interacting objects sharing a common environment. The evolution of each object is determined by a stochastic difference equation where the random disturbance density $$\rho $$ ρ is unknown for the controller. We present the Markov control model (N-model) associated to the proportions of objects in each state, which is analyzed according to the mean field theory. Thus, combining convergence results as $$N\rightarrow \infty $$ N → ∞ (the mean field limit) with a suitable statistical estimation method for $$\rho $$ ρ , we construct the so-named eventually asymptotically optimal policies for the N-model under a discounted optimality criterion. A consumption-investment problem is analyzed to illustrate our results.
Applied Mathematics and Optimization – Springer Journals
Published: Sep 7, 2015
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