We reveal an interesting convex duality relationship between two problems: (a) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market; (b) a controller-and-stopper problem, in which the...

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...