Option pricing formulas based on uncertain fractional differential equation |
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Authors: | Wang Weiwei Ralescu Dan A |
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Institution: | 1.Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai, 200000, China ;2.Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025, USA ; |
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Abstract: | Uncertain fractional differential equations have been playing an important role in modelling complex dynamic systems. Early researchers have presented the extreme value theorems and time integral theorem on uncertain fractional differential equation. As applications of these theorems, this paper investigates the pricing problems of American option and Asian option under uncertain financial markets based on uncertain fractional differential equations. Then the analytical solutions and numerical solutions of these option prices are derived, respectively. Finally, some numerical experiments are performed to verify the effectiveness of our results. |
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