摘要翻译：
提出了金融期权定价的自适应波动模型，作为标准Black-Scholes模型的高复杂度替代。新的期权定价模型表示受控布朗运动，包括非线性和量子两种波型方法，它们都基于Schr-Odinger方程的自适应形式，非线性方法分为两种：（一）对于恒定波动率，它由一个自适应非线性Schr-Odinger方程定义；对于随机波动率，它由两个耦合NLS方程的自适应Manakov系统定义。线性量子方法是根据德布罗意平面波和自由粒子Schr-Odinger方程定义的。在这种方法中，金融变量具有量子力学解释，满足海森堡型不确定性关系。这两种模型都能够成功地拟合Black-Scholes数据，并能够定义希腊人。关键词：Black-Scholes期权定价，自适应非线性Schr-Odinger方程，自适应Manakov系统，量子力学期权定价，市场热势PACS:89.65.GH,05.45.YV,03.65.GE
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英文标题：
《Adaptive Wave Models for Option Pricing Evolution: Nonlinear and Quantum
  Schr\"odinger Approaches》
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作者：
Vladimir G. Ivancevic
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最新提交年份：
2010
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分类信息：

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：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black--Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear and quantum, both based on (adaptive form of) the Schr\"odinger equation. The nonlinear approach comes in two flavors: (i) for the case of constant volatility, it is defined by a single adaptive nonlinear Schr\"odinger (NLS) equation, while for the case of stochastic volatility, it is defined by an adaptive Manakov system of two coupled NLS equations. The linear quantum approach is defined in terms of de Broglie's plane waves and free-particle Schr\"odinger equation. In this approach, financial variables have quantum-mechanical interpretation and satisfy the Heisenberg-type uncertainty relations. Both models are capable of successful fitting of the Black--Scholes data, as well as defining Greeks.   Keywords: Black--Scholes option pricing, adaptive nonlinear Schr\"odinger equation, adaptive Manakov system, quantum-mechanical option pricing, market-heat potential   PACS: 89.65.Gh, 05.45.Yv, 03.65.Ge
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PDF链接：
https://arxiv.org/pdf/1001.0615