We extend the dynamic Cournot model of Ludkovski and Sircar (2012) by considering stochastic demand. We analyze a duopoly between an exhaustible producer and a "green" competitor. Both producers dynamically make decisions regarding their production rates; in addition the exhaustible producer...

We apply stochastic Perron's method to a singular control problem where an individual targets at a given consumption rate, invests in a risky financial market in which trading is subject to proportional transaction costs, and seeks to minimize her probability of lifetime ruin. Without relying on...

We analyze an optimal stopping problem with random maturity $\tau_0$ under a nonlinear expectation over a weakly compact set of mutually singular probabilities. The maturity $\tau_0$ is specified as the hitting time to level 0 of some continuous index process $X$ at which the payoff process $Y$...