英文标题：
《Second order stochastic differential models for financial markets》
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作者：
Nguyen Tien Zung
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最新提交年份：
2017
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英文摘要：
  Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations which describe the motion of financial prices with respect to real world probability measures should be of second order (and non-Markovian), instead of first order models \\`a la Bachelier--Samuelson. Our theoretical result in stochastic dynamical systems shows that one cannot correctly reduce second order models to first order models by simply forgetting about momenta. We propose some simple second order models, including a stochastic constrained n-oscillator, which can explain many market phenomena, such as boom-bust cycles, stochastic quasi-periodic behavior, and \"hot money\" going from one market sector to another.
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中文摘要：
利用基于主体的建模、经验证据和物理思想，如能量函数和相空间必须具有两倍于配置空间维数的事实，我们认为，描述金融价格相对于真实世界概率测度的运动的随机微分方程应为二阶（非马尔可夫），而不是一阶模型——一个单身汉——萨缪尔森。我们在随机动力系统中的理论结果表明，仅仅忘记动量是不能正确地将二阶模型简化为一阶模型的。我们提出了一些简单的二阶模型，包括一个随机约束的n-振子，它可以解释许多市场现象，如繁荣-萧条周期、随机准周期行为和“热钱”从一个市场部门流向另一个市场部门。
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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：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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一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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