A duopoly preemption game with two alternative stochastic investment choices

This paper studies a duopoly investment model with uncertainty. There are two alternative irreversible investments. The first firm to invest gets a monopoly benefit for a specified period of time. The second firm to invest gets information based on what happens with the first investor, as well as cost reduction benefits. We describe the payoff functions for both the leader and follower firm. Then, we present a stochastic control game where the firms can choose when to invest, and hence influence whether they become the leader or the follower. In order to solve this problem, we combine techniques from optimal stopping and game theory. For a specific choice of parametres, we show that no pure symmetric subgame perfect Nash equilibrium exists. However, an asymmetric equilibrium is characterized. In this equilibrium, two disjoint intervals of market demand level give rise to preemptive investment behavior of the firms, while the firms otherwise are more reluctant to be the first mover

Stochastic maximum principle with Lagrange multipliers and optimal consumption with Lévy wage

We show how a stochastic version of the Lagrange multiplier method can be combined with the stochastic maximum principle for jump diffusions to solve certain constrained stochastic optimal control problems. Two different terminal constraints are considered; one constraint holds in expectation and the other almost surely. As an application of this method, we study the effects of inflation- and wage risk on optimal consumption. To do this, we consider the optimal consumption problem for a budget constrained agent with a Lévy income process and stochastic inflation. The agent must choose a consumption path such that his wealth process satisfies the terminal constraint. We find expressions for the optimal consumption of the agent in the case of CRRA utility, and give an economic interpretation of the adjoint processes. The final publication is available at Springer via http://dx.doi.org/10.1007/s13370-015-0360-

A Dynamic Market Model

This paper looks at a dynamic process in a partial market where there are lags in the adjustment of the consumers as a group, and where the firms are not perfectly equal. What I model is the movements of price and realized quantum of a market good given the allocation of the demand and supply curves. A major conclusion is that given the circumstances, the system will always converge to the equilibrium point in the long run, but if shocks occur, the market allocation of price and realized quantum of the good may very well remain in disequilibrium. Unless one studies a particular market, it is not possible to make a precise general description of how the movements in disequilibrium behave quantitatively and describe the speed of convergence to equilibrium. However, qualitative conclusions are more easily drawn on a general basis

A duopoly preemption game with two alternative stochastic investment choices

This paper studies a duopoly investment model with uncertainty. There are two alternative irreversible investments. The first firm to invest gets a monopoly benefit for a specified period of time. The second firm to invest gets information based on what happens with the first investor, as well as cost reduction benefits. We describe the payoff functions for both the leader and follower firm. Then, we present a stochastic control game where the firms can choose when to invest, and hence influence whether they become the leader or the follower. In order to solve this problem, we combine techniques from optimal stopping and game theory. For a specific choice of parametres, we show that no pure symmetric subgame perfect Nash equilibrium exists. However, an asymmetric equilibrium is characterized. In this equilibrium, two disjoint intervals of market demand level give rise to preemptive investment behavior of the firms, while the firms otherwise are more reluctant to be the first mover