Abstract
Risk is usually a criteria which involves the world’s state; for instance the best policy to extract oil from a well of finite resource depends on the price of oil which in turn depends on how much the world’s oil extractors produce. Many optimization of systems with respect to profit and risk involve a very large number of players who optimize the same criteria. Then the profit is the result of a global optimization problem, which is coupled with a each player’s system design where price appears as a passive variable. Meanfield type control is a mathematical tool which can help solve such problem in the presence of randomness, an aspect essential for the modeling of risk. We shall give a few examples and compare solutions by calculus of variations plus gradient algorithms with extended dynamic programming and fixed point.
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Pironneau, O., Laurière, M. (2019). Risk, Optimization and Meanfield Type Control. In: Minisci, E., Vasile, M., Periaux, J., Gauger, N., Giannakoglou, K., Quagliarella, D. (eds) Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Computational Methods in Applied Sciences, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-319-89988-6_1
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