摘要翻译:
在路径积分的框架下,构造了Merton-Garman哈密顿算子的演化算子核。在此基础上得到了核期权公式,推广了著名的Black-Scholes结果。提出了路径积分计算的可能的近似数值格式。
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英文标题:
《The path integral representation kernel of evolution operator in
Merton-Garman model》
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作者:
L. F. Blazhyevskyi, V. S. Yanishevsky
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最新提交年份:
2011
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分类信息:
一级分类:Physics 物理学
二级分类:Mathematical Physics 数学物理
分类描述:Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域,为这类应用开发数学方法,或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣;主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类:Mathematics 数学
二级分类:Mathematical Physics 数学物理
分类描述:math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域,为这类应用开发数学方法,或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣;主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类:Quantitative Finance 数量金融学
二级分类:Pricing of Securities 证券定价
分类描述:Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要:
In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.
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PDF链接:
https://arxiv.org/pdf/1106.5143