Invited Session Wed.1.MA 549

Wednesday, 10:30 - 12:00 h, Room: MA 549

Cluster 18: Optimization in energy systems [...]

Games, energy and investment


Chair: Rene Aid



Wednesday, 10:30 - 10:55 h, Room: MA 549, Talk 1

Vincent Leclère
The priority option: The value of being a leader in complete and incomplete markets

Coauthors: Matheus Grasselli, Mike Ludkovski


In a recent paper, Bensoussan, Diltz and Hoe (2010) provide a comprehensive analysis of optimal investment strategies under uncertainty and competition. They consider two firms competing for a project whose payoff can be either a lump-sum or a series of cash-flows, in both complete and incomplete markets. Despite its generality, the analysis is restricted to a Stackelberg game, where the roles of leader and follower are predetermined. In this talk, I'll extend the analysis to the case where these roles emerge as the result of a symmetric, Markov, sub-game perfect equilibrium, extending the seminal work of Grenadier (1996) and (2000) to incomplete markets. As a result, one can calculate the amount of money that a firm would be willing to spend in advance (either by paying a license or acquiring market power) to have the right to be the leader in a subsequent game - what we call the priority option.



Wednesday, 11:00 - 11:25 h, Room: MA 549, Talk 2

Xiaolu Tan
A splitting scheme for degenerate nonlinear PDEs: Application in an optimal hydropower management problem


Based on the semi-Lagrangian scheme and the probabilistic scheme of Fahim, Touzi and Warin for non-degenerate fully nonlinear parabolic PDEs, we propose a splitting numerical method for degenerate nonlinear parabolic PDEs. We also provide a simulation-regression method to make the splitting scheme implementable. General convergence as well as rate of convergence are obtained under reasonable conditions, using the monotone convergence of viscosity solution techniques. Finally, we study an optimal hydropower management problem which can be characterized by a degenerate nonlinear parabolic PDE. A numerical resolution is given by this splitting method.



Wednesday, 11:30 - 11:55 h, Room: MA 549, Talk 3

Imen Ben Tahar
Integration of an intermittent energy: A mean fields game approach


The integration of renewable sources of energy to the grid brings new challenges, due to
their intermittent nature. In this talk we propose a toy model, based on a mean fields games (MFG)
approach, to analyze consumption decisions integrating a stochastic source of energy


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