We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games finds natural applications in the context of optimal...

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games finds natural applications in the context of optimal...

This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated Itô-diffusion via a two-sided singular stochastic control and faces a long-time-average expected profit criterion....

We revisit the influential economic growth model by Lucas (1988) ["On the mechanics of economic development." Journal of Monetary Economics, 22(1):3-42], assuming that households optimally allocate consumption and education over the life-cycle given an exogenous interest rate and exogenous...

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 consider a class of N-player stochastic games of multi-dimensional singular control, in which each player faces a minimization problem of monotone-follower type with submodular costs. We call these games monotone-follower games. In a not necessarily Markovian setting, we establish the...

Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash flows are discounted at a stochastic dynamic rate. Dividends can be paid to shareholders at unrestricted rates so that...

This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated Itô-diffusion via a two-sided singular stochastic control and faces a long-time-average expected profit criterion....

We revisit the influential economic growth model by Lucas (1988) ["On the mechanics of economic development." Journal of Monetary Economics, 22(1):3-42], assuming that households optimally allocate consumption and education over the life-cycle given an exogenous interest rate and exogenous...