Mean-Field Leader-Follower Games with Terminal State Constraint

Abstract

We analyze linear McKean--Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted spaces as well as a convergence result of the solutions with respect to certain perturbations of the drivers of both the forward and the backward component. The general results are used to solve a novel single player model of portfolio liquidation under market impact with expectations feedback as well as a novel Stackelberg game of optimal portfolio liquidation with asymmetrically informed players.

A Maximum Principle approach to deterministic Mean Field Games of Control with Absorption

“…Due to the non-negativity constraint on the state process, the Hamiltonian depends on the initial condition, while the terminal value of the adjoint process is unknown. The latter is very similar to portfolio liquidation models where the terminal condition of the adjoint process is unknown, due to the liquidation constraint; see [11,12] for details. In order to overcome this problem we consider the Hamiltonian only up a candidate optimal exploitation time.…”

Price Formation and Optimal Trading in Intraday Electricity Markets

“…Interestingly, when the players don't have a terminal penalty (λ = λ 0 = 0), the equilibrium positions of the agents in equation (13) still contain forward looking terms, which were absent in the case of the mean field game with identical players (see Equation 5with λ = 0). The presence of these terms is due to the strategic interaction of the major player with the mean field of small agents.…”

Equilibrium price formation with a major player and its mean field limit

“…One can find in [1,14,16,21,24,32,45] interesting applications to, optimal trading, liquidation, energy production, optimal use of smart grids, etc. In particular, we refer to Fu & Horst [25], Evangelista & Thamsten [19] and Féron et.al. [22] who studied the optimal liquidation and trading problems in the mean-field games with a major player.…”