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...

In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework within which to value derivatives under market impact in a multi-player framework by introducing strategic...

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...