  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.
