英文标题：
《PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black-Scholes
  Equation》
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作者：
Will Hicks
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最新提交年份：
2019
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英文摘要：
  The Accardi-Boukas quantum Black-Scholes framework, provides a means by which one can apply the Hudson-Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via a Kramers-Moyal expansion, and this provides useful tools to understand their behaviour. In this paper we develop further links between quantum stochastic processes, and nonlocal diffusions, by inverting the question, and showing how certain nonlocal diffusions can be written as quantum stochastic processes. We then go on to show how one can use path integral formalism, and PT symmetric quantum mechanics, to build a non-Gaussian kernel function for the Accardi-Boukas quantum Black-Scholes. Behaviours observed in the real market are a natural model output, rather than something that must be deliberately included.
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中文摘要：
Accardi-Boukas量子Black-Scholes框架提供了一种方法，可以将Hudson Parthasarathy量子随机微积分应用于金融问题。通过Kramers-Moyal展开，可以使用非局部扩散过程对这些方程的解进行建模，这为理解它们的行为提供了有用的工具。在本文中，我们通过反转问题，进一步发展了量子随机过程与非局部扩散之间的联系，并展示了某些非局部扩散如何可以写成量子随机过程。然后，我们继续展示如何使用路径积分形式和PT对称量子力学为Accardi-Boukas量子Black-Scholes构建非高斯核函数。在真实市场中观察到的行为是一种自然的模型输出，而不是必须故意包含在内的东西。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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