模糊环境下多维跳跃扩散市场模型的欧式极大看涨期权定价

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 343-358.

模糊环境下多维跳跃扩散市场模型的欧式极大看涨期权定价

刘红卫¹^,²^,³, 王亚军¹, 马鹏程¹^,^*()

¹桂林电子科技大学数学与计算科学学院广西桂林 541004
²广西高校数据分析与计算重点实验室广西桂林 541004
³广西应用数学中心 (桂林电子科技大学) 广西桂林 541004

收稿日期:2024-09-11 修回日期:2025-04-15 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 马鹏程 E-mail:lhw_28@163.com
基金资助:
广西科技计划项目(Guike AD25069086);广西自然科学基金(2025GXNSFAA069661)

European Maximal Call Options Pricing in a Multidimensional Jump Diffusion Market Model Under a Fuzzy Environment

Hongwei Liu¹^,²^,³, Yajun Wang¹, Pengcheng Ma¹^,^*()

¹School of Mathematics and Computing Science, Guilin University of Electronic Technology, Nanning Guilin 541004
²Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Nanning Guilin 541004
³Center for Applied Mathematics of Guangxi (GUET), Nanning Guilin 541004

Received:2024-09-11 Revised:2025-04-15 Online:2026-02-26 Published:2026-01-19
Contact: Pengcheng Ma E-mail:lhw_28@163.com
Supported by:
Science and Technology Project of Guangxi(Guike AD25069086);Guangxi Natural Science Foundation(2025GXNSFAA069661)

摘要/Abstract

摘要：

文章将模糊性和随机性相结合来刻画多维欧式极大看涨期权的不确定性. 研究了在跳跃幅度为模糊对数正态和模糊双指数分布情形下, 利用 L$\acute{\rm e}$vy-It$\hat{\rm o}$ 公式给出了相应的欧式极大看涨期权的定价公式. 在对模糊期权估值中, 通过加权概率平均, 给出了一个清晰数. 最后通过数值模拟分析了主要参数变化和不同模型对欧式极大看涨期权定价的影响.

关键词: 模糊随机变量, 模糊对数正态分布, 模糊双指数分布, 欧式极大看涨期权

Abstract:

In this paper, the uncertainty of the multidimensional European maximal call option is characterized by a combination of fuzziness and stochasticity. The pricing formulas for the correspond-ing European maximal call option are given by L$\acute{\rm e}$vy-It$\hat{\rm o}$ formula, when the logarithm of the jump amplitude is with fuzzy normal sum and fuzzy double exponential distribution. A clarity number is given by weighted probability averaging in the valuation of the fuzzy option. Finally, the effects of the variation of the main parameters and different models on the pricing of the European maximal call option are analyzed by numerical simulation.

Key words: fuzzy random variables, fuzzy Lognormal distribution, fuzzy double exponential distribution, European maximal call option

中图分类号:

O211

刘红卫, 王亚军, 马鹏程. 模糊环境下多维跳跃扩散市场模型的欧式极大看涨期权定价[J]. 数学物理学报, 2026, 46(1): 343-358.

Hongwei Liu, Yajun Wang, Pengcheng Ma. European Maximal Call Options Pricing in a Multidimensional Jump Diffusion Market Model Under a Fuzzy Environment[J]. Acta mathematica scientia,Series A, 2026, 46(1): 343-358.

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