A stochastic maximum principle for a stochastic differential game of a mean-field type

DOI10.1007/s00245-012-9177-xzbMath1261.49005OpenAlexW2087989961MaRDI QIDQ1935504

John Joseph Absalom Hosking

Publication date: 18 February 2013

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-00641090/file/A_stochastic_maximum_principle_for_a_stochastic_differential_game_of_a_mean-field_type_by_John_J._A._Hosking.pdf

zbMATH Keywords

Nash equilibriastochastic maximum principlestochastic differential gamesadjoint processesmean-field type backward stochastic equationsmean-field type stochasic equations

Mathematics Subject Classification ID

Differential games and control (49N70) Optimal stochastic control (93E20) Stochastic games, stochastic differential games (91A15) Stochastic calculus of variations and the Malliavin calculus (60H07) Optimality conditions for problems involving randomness (49K45)

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Mean-field stochastic linear-quadratic optimal control with Markov jump parameters ⋮ Mean-field-type games with jump and regime switching ⋮ Risk-sensitive mean-field-type games with \(L^p\)-norm drifts ⋮ Behavior Near Walls in the Mean-Field Approach to Crowd Dynamics ⋮ Stochastic \(H_2/H_{\infty}\) control for mean-field stochastic differential systems with \((x, u, v)\)-dependent noise ⋮ Berge equilibrium in linear-quadratic mean-field-type games ⋮ Risk-Sensitive Mean-Field Type Control Under Partial Observation ⋮ Mean-field linear-quadratic stochastic differential games in an infinite horizon ⋮ A maximum principle for mean-field stochastic control system with noisy observation ⋮ Mean-field-type games

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