Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 534, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.physa.2019.122357
Keywords
Fractional differential equation; Uncertainty theory; Extreme value; Simpson method; Option pricing; Stock model
Categories
Funding
- National Natural Science Foundation of China [61673011]
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Uncertain fractional differential equation plays an important role of describing uncertain dynamic process. This paper focuses on extreme values (including supremum and infimum) for solution to an uncertain fractional differential equation for the Caputo type. Theorems for the inverse uncertain distributions of the extreme values are given based on the definition of a-path. And then, numerical algorithms for them are designed, numerical examples are shown for validating the availability about algorithms. The absolute errors between the numerical and analytical results are also presented to demonstrate the accuracy of the algorithms. Finally, as an application of the extreme values, an uncertain stock model is proposed on the basis of uncertain fractional differential equation of the Caputo type. The American option pricing formulas of such stock model are studied by using the proposed extreme theorems. Besides, numerical calculations are also illustrated with respect to different parameters p. (C) 2019 Elsevier B.V. All rights reserved.
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