We analyze novel portfolio liquidation games with self-exciting order flow. Both the N-player game and the mean-field game are considered. We assume that players' trading activities have an impact on the dynamics of future market order arrivals thereby generating an additional transient price...

This paper establishes the existence of relaxed solutions to mean eld games (MFGs for short) with singular controls. As a by-product, we obtain an existence of relaxed solutions results for McKean-Vlasov stochastic singular control problems. Finally, we prove approximations of solutions results...

This paper establishes the existence of relaxed solutions to mean eld games (MFGs for short) with singular controls. As a by-product, we obtain an existence of relaxed solutions results for McKean-Vlasov stochastic singular control problems. Finally, we prove approximations of solutions results...

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...

We analyze novel portfolio liquidation games with self-exciting order flow. Both the N-player game and the mean-field game are considered. We assume that players' trading activities have an impact on the dynamics of future market order arrivals thereby generating an additional transient price...

We state conditions for existence and uniqueness of equilibria in evolutionary models with an infinity of locally and globally interacting agents. Agents face repeated discrete choice problems. Their utility depends on the actions of some designated neighbors and the average choice throughout...

We give sufficient conditions for a non-zero sum discounted stochastic game with compact and convex action spaces and with norm-continuous transition probabilities, but with possibly unbounded state space to have a N ash equilibrium in homogeneous Markov strategies that depends in a Lipsehitz...

We consider the stochastic sequence {Yi}t E N defined recursively by the linear relation Yt+l = AtYt + Bt in a random environment. The environment is described by the stochastic process {(At, Bt ) }t E N and is under the simultaneous control of several agents playing a discounted stochastic...

In this paper we consider the stochastic sequence {Pt}E N defined recursively by the linear relation Pt+1 = At Pt + Bt in a random environment which is described by the non-stationary process V = {(At, Bt) t E N.. We formulate sufficient conditions on v which ensure that the finite-dimensional...