英文标题：
《Towards a formalization of a two traders market with information
  exchange》
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作者：
F. Bagarello, E. Haven
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最新提交年份：
2014
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英文摘要：
  This paper shows that Hamiltonians and operators can also be put to good use even in contexts which are not purely physics based. Consider the world of finance. The work presented here {models a two traders system with information exchange with the help of four fundamental operators: cash and share operators; a portfolio operator and an operator reflecting the loss of information. An information Hamiltonian is considered and an additional Hamiltonian is presented which reflects the dynamics of selling/buying shares between traders. An important result of the paper is that when the information Hamiltonian is zero, portfolio operators commute with the Hamiltonian and this suggests that the dynamics are really due to the information. Under the assumption that the interaction and information terms in the Hamiltonian have similar strength, a perturbation scheme is considered on the interaction parameter. Contrary to intuition, the paper shows that up to a second order in the interaction parameter, a key factor in the computation of the portfolios of traders will be the initial values of the loss of information (rather than the initial conditions on the cash and shares). Finally, the paper shows that a natural outcome from the inequality of the variation of the portfolio of trader one versus the variation of the portfolio of trader two, begs for the introduction of `good\' and `bad\' information. It is shown that `good\' information is related to the reservoirs (where an infinite set of bosonic operators are used) which model rumors/news and external facts, whilst `bad\' information is associated with a set of two modes bosonic operators.
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中文摘要：
本文表明，即使在不完全基于物理的环境中，哈密顿量和算符也可以很好地使用。想想金融世界吧。这里展示的作品{在四个基本算子（现金和股票算子、投资组合算子和反映信息损失的算子）的帮助下，建立了一个具有信息交换的两个交易者系统模型。考虑了一个信息哈密顿量，并给出了一个反映交易者之间股票买卖动态的附加哈密顿量。本文的一个重要结果是信息哈密顿量为零，投资组合算子与哈密顿量相互转换，这表明动态实际上是由信息引起的。在假设哈密顿量中的相互作用项和信息项具有相似强度的情况下，考虑了相互作用参数的摄动格式。与直觉相反，本文表明，在交互参数高达二阶时，计算交易者投资组合的一个关键因素将是信息损失的初始值（而不是现金和股票的初始条件）。最后，本文表明，交易员一的投资组合变化与交易员二的投资组合变化不相等的自然结果要求引入“好”和“坏”信息。研究表明，“好”信息与模拟谣言/新闻和外部事实的水库（其中使用了无限多个玻色子算符）有关，而“坏”信息与一组双模玻色子算符有关。
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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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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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