Optimal Multi-Modes Switching with the Switching Cost not necessarily Positive

Details Optimal Multi-Modes Switching with the Switching Cost not necessarily Positive Optimal Multi-Modes Switching with the Switching Cost not necessarily Positive

2012-04-07

arxiv.org/abs/1204.1683v1

Mathematics

Optimization and Control

26 pages. arXiv admin note: substantial text overlap with arXiv:1102.1256, arXiv:0805.1306, arXiv:0904.0707, arXiv:1202.1108,

Scientific paper

In this paper, we study the $m$-states optimal switching problem in finite horizon, when the switching cost functions are arbitrary and can be positive or negative. This has an economic incentive in terms of central evaluation in cases where such organizations or state grants or financial assistance to power plants that promotes green energy in their production activity or what uses less polluting modes in their production. We show existence for optimal strategy via a verification theorem then we show existence and uniqueness of the value processes by using an approximation scheme. In the markovian framework we show that the value processes can be characterized in terms of deterministic continuous functions of the state of the process. Those latter functions are the unique viscosity solutions for a system of $m$ variational partial differential inequalities with inter-connected obstacles.

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