Real Options Of Water Management Fitted Finite Volume Methods

As is known to us, agricultural activities are most affcted by climate change obv-iously and directly. It becomes increasingly important to manage water and improve the effciency of irrigation with higher temperatures and irregular precipitation patterns. Followed by increasing environmental demands on water, agriculture must improve water use effciency generally as soon as possible. In this paper, we use a real options approach to establish a model to handle future uncertainties about the water price. In addition, to match the practical situation, the expiration of the real option is conside-red in our model. Then, we reformulate the problem to a linear parabolic variational inequality (VI).and develop a power penalty method to solve it. Thus, a nonlinear par-tial differential equation(PDE). which is shown to be uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O(λ-k/2). Furthermore, a so-called fitted finite volume method is proposed to solve the nonlinear PDE. Finally, sev-eral numerical experiments are performed to illustrate the effciency and the usefulness of this method aswell as the impacts of main parameters on the timing of investments.