Degenerate Variance Control in the One-dimensional Stationary Case
Daniel L Ocone, Rutgers University
Ananda Weerasinghe, Iowa State University
Abstract
We study the problem of stationary control by adaptive choice of the diffusion coefficient
in the case that control degeneracy is allowed and the drift admits a unique, asymptotically
stable equilibrium point. We characterize the optimal value and obtain it as an
Abelian limit of optimal discounted values and as a limiting average of finite horizon optimal
values, and we also characterize the optimal stationary strategy. In the case of linear drift,
the optimal stationary value is expressed in terms of the solution of an optimal stopping
problem. We generalize the above results to allow unbounded cost functions.
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