一个金融市场,单一的漂移,没有套利
Nacira Agram1, Bernt Øksendal2
1Department of Mathematics, Linnaeus University, SE-351 95 Växjö, Sweden.
概括
本研究引入了一个带有延迟的跳跃扩散市场模型,在存在延迟时没有找到套利机会. 然而,随着延迟接近零,套利变得可能,反映没有延迟的模型.
科学领域:
- 量化金融 量化金融
- 数学金融数学金融
- 金融建模金融建模
背景情况:
- 金融市场可以表现出复杂的动态,包括跳跃和延迟,这对于现实的建模至关重要.
- 以前的单一漂移模型,如几何Itô-Lévy过程,引起了对市场套利的担忧,特别是在连续设置中.
- 这些模型中跳跃和信息流延迟对市场套利的影响仍然不清楚.
研究的目的:
- 开发和分析一个跳跃扩散市场模型,包括单一的漂移术语和信息流中的延迟.
- 调查这种延迟的市场模型中是否存在套利机会.
- 计算最佳的消费和投资组合策略,并确定市场的最大价值.
主要方法:
- 使用白噪声计算来分析金融市场模型.
- 风险资产的建模采用几何Itô-Lévy过程,具有单一的漂移术语.
- 结合布朗运动和Poisson随机测量跳跃,以及延迟参数.
主要成果:
- 当延迟参数不等于零时,市场的最大值是有限的,表明没有套利.
- 随着延迟接近零,最大值倾向于无限,这表明套利的重新出现.
- 最佳的消费率和投资组合是明确使用开发的数学框架计算的.
结论:
- 信息流中的延迟可以防止金融市场跳跃扩散中的套利.
- 该模型为理解有或没有延迟的市场中套利动态提供了一个框架.
- 这些发现与高频交易有关,高频交易中,无限小的时间尺度可以导致奇异的漂移.
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