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   https://doi.org/10.23919/ACC.2019.8814842  

   Gupta, Piyush ; Srivastava, Vaibhav ( July 2019 , 2019 American Control Conference (ACC))

   We study optimal fidelity selection for a human operator servicing a queue of homogeneous tasks. The service time distribution of the human operator depends on her cognitive dynamics and the level of fidelity selected for servicing the task. Cognitive dynamics of the operator evolve as a Markov chain in which the cognitive state increases (decreases) with high probability whenever she is busy (resting). The tasks arrive according to a Poisson process and each task waiting in the queue loses its value at a fixed rate. We address the trade-off between high quality service of a task and consequent loss in value of future tasks using a Semi-Markov Decision Process (SMDP) framework. We numerically determine an optimal policy and establish its structural properties. 

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2. Linear quadratic stochastic optimal control problems with operator coefficients: open-loop solutions

   https://doi.org/10.1051/cocv/2018013  

   Wei, Qingmeng ; Yong, Jiongmin ; Yu, Zhiyong ( January 2019 , ESAIM: Control, Optimisation and Calculus of Variations)

   An optimal control problem is considered for linear stochastic differential equations with quadratic cost functional. The coefficients of the state equation and the weights in the cost functional are bounded operators on the spaces of square integrable random variables. The main motivation of our study is linear quadratic (LQ, for short) optimal control problems for mean-field stochastic differential equations. Open-loop solvability of the problem is characterized as the solvability of a system of linear coupled forward-backward stochastic differential equations (FBSDE, for short) with operator coefficients, together with a convexity condition for the cost functional. Under proper conditions, the well-posedness of such an FBSDE, which leads to the existence of an open-loop optimal control, is established. Finally, as applications of our main results, a general mean-field LQ control problem and a concrete mean-variance portfolio selection problem in the open-loop case are solved. 

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3. Optimal bailouts and the doom loop with a financial network

   https://doi.org/10.1016/j.jmoneco.2022.03.004  

   Capponi, Agostino ; Corell, Felix ; Stiglitz, Joseph E. ( May 2022 , Journal of Monetary Economics)
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   Sivaramakrishnan, Vignesh ; Vinod, Abraham P. ; Oishi, Meeko M. ( June 2023 , IEEE Transactions on Automatic Control)
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   https://doi.org/10.1007/s00285-020-01501-1  

   Wilson, Dan ( July 2020 , Journal of Mathematical Biology)