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We investigated a cost-constrained static ergodic control problem of thevariance of measure-valued affine processes and its application in streamflowmanagement. The controlled system is a jump-driven mixed moving average processthat generates realistic subexponential autocorrelation functions, and thestatic nature of the control originates from a realistic observabilityassumption in the system. The Markovian lift was effectively used to discretizethe system into a finite-dimensional process, which is easier to analyze. Theresolution of the problem is based on backward Kolmogorov equations and aquadratic solution ansatz. The control problem has a closed-form solution, andthe variance has both strict upper and lower bounds, indicating that thevariance cannot take an arbitrary value even when it is subject to a highcontrol cost. The correspondence between the discretized system based on theMarkovian lift and the original infinite-dimensional one is discussed. Then, aconvergent Markovian lift is presented to approximate the infinite-dimensionalsystem. Finally, the control problem was applied to real cases using availabledata for a river reach. An extended problem subject to an additional constrainton maintaining the flow variability was also analyzed without significantlydegrading the tractability of the proposed framework.

Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments