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...

This paper proposes a strategic model of pollution control. A firm, representative of the productive sector of a country, aims at maximizing its profits by expanding its production. Assuming that the output of production is proportional to the level of pollutants' emissions, the firm increases...

We consider the problem of a government that wants to manage the country's debt-to- GDP (gross domestic product) ratio. The latter evolves stochastically in continuous time, and its drift is given by the interest rate on government debt, net of the growth rate of GDP. We further allow the...

Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads to a proportional cost whose instantaneous marginal value...

In this paper we propose and solve an optimal dividend problem with capital injections over a finite time horizon. The surplus dynamics obeys a linearly controlled drifted Brownian motion that is reflected at zero, dividends give rise to time-dependent instantaneous marginal profits, whereas...

This paper studies an optimal irreversible extraction problem of an exhaustible commodity in presence of regime shifts. A company extracts a natural resource from a reserve with finite capacity, and sells it in the market at a spot price that evolves according to a Brownian motion with...

We consider a government that aims at reducing the debt-to-gross domestic product (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic...

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 deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process v whose components have paths of bounded variation. The presence of the process v prevents from directly applying classical results and novel estimates need to be...