Abstract
With the climate change processes over times, all professions and trades in Three Gorges Reservoir Area will be influenced. One of the biggest challenges is the risk of rising sea level. In this situation, a large number of uncertainties for climate changes will be faced in Three Gorges Reservoir Area. Therefore, it is of importance to investigate the complexity of decision making on investing in the long term rising sea level risk related projects in Three Gorges Reservoir Area. This paper investigates the sea level and the temperature as the underlying assets in Three Gorges Reservoir Area. A real option model is constructed to evaluate potential sea level rising risk. We formulate European and American real option models into a linear parabolic variational inequalities and propose a power penalty approach to solve it. Then we obtain a nonlinear parabolic equation. It shows that the nonlinear parabolic equation is unique and solvable. Also, the solutions of the nonlinear parabolic equation converge to the solutions of the parabolic variational inequalities at the rate of order O(λ−k/2). Since the analytic solution of nonlinear parabolic equation is difficult to obtain, a fitted finite volume method is developed to solve it in case of European and American options, and the convergence of the nonlinear parabolic equation is obtained. An empirical analysis is presented to illustrate our theoretical results.
Funding statement: This work is supported by National Science Foundation of China (11201510), National Social Science Fund of China (19BGL190), China Postdoctoral Science Foundation (2017T100155, 2015M580197), Innovation Team Building at Institutions of Higher Education in Chongqing (CXTDX201601035), Chongqing Research Program of Basic Research and Frontier Technology (cstc2019jcyj-msxmX0280), Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJZD-K202001201) and Hunan Provincial Education Department of China (18C0196).
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Data availability. The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Competing interests. The authors declare that they have no competing interests.
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Authors’ contributions. Huang Fei and Lu Zuliang have participated in the sequence alignment and drafted the manuscript. Li lin, Wu Xiankui, and Liu Shang have made substantial contributions to conception and design.
Acknowledgment
The authors express their thanks to the referees for their helpful suggestions,which led to improvements of the presentation. The authors express their thanks to Babatunde O. Onsanya for his helpful advices on professional language editing.
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