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Numerical simulation for European and American option of risks in climate change of Three Gorges Reservoir Area
Journal of Numerical Mathematics ( IF 3 ) Pub Date : 2022-03-01 , DOI: 10.1515/jnma-2020-0081
Fei Huang 1 , Zuliang Lu 1, 2 , Lin Li 3 , Xiankui Wu 1 , Shang Liu 4 , Yin Yang 5
Affiliation  

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.

中文翻译:

三峡库区气候变化风险欧美期权的数值模拟

随着时间的推移,气候变化的进程,将影响三峡库区的各行各业。最大的挑战之一是海平面上升的风险。在这种情况下,三峡库区将面临大量气候变化的不确定性。因此,研究三峡库区长期海平面上升风险相关项目投资决策的复杂性具有重要意义。本文将海平面和温度作为三峡库区的标的资产进行调查。建立实物期权模型来评估潜在的海平面上升风险。我们将欧式和美式实物期权模型化为线性抛物变分不等式,并提出一种幂惩罚方法来解决它。然后我们得到一个非线性抛物方程。它表明非线性抛物方程是唯一的和可解的。此外,非线性抛物方程的解以 O ( λ - k /2 ) 阶的速率收敛到抛物变分不等式的解。由于非线性抛物方程的解析解难以获得,在欧式和美式期权的情况下,发展了一种拟合有限体积法求解,得到了非线性抛物方程的收敛性。给出了一个实证分析来说明我们的理论结果。由于非线性抛物方程的解析解难以获得,在欧式和美式期权的情况下,发展了一种拟合有限体积法求解,得到了非线性抛物方程的收敛性。给出了一个实证分析来说明我们的理论结果。由于非线性抛物方程的解析解难以获得,在欧式和美式期权的情况下,发展了一种拟合有限体积法求解,得到了非线性抛物方程的收敛性。给出了一个实证分析来说明我们的理论结果。
更新日期:2022-03-01
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