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摘要翻译：
我们提出了两个具有异质套利者和正反馈的瞬态金融泡沫的理性预期模型，该模型导致了自增强的瞬态随机快于指数的价格动态。非线性反馈的结果表明，泡沫价格形成过程在某个潜在的临界时刻$\tilde{t}_c$结束时具有有限时间奇异性，并遵循均值反向平稳动力学。由于理性主体期望的异质性，套利者确定的最优退出时间存在同步问题，导致泡沫几乎一直存活到理论终结时间。这两个模型的显式精确解析解提供了非线性变换，使我们能够对金融时间序列中泡沫的存在进行新的检验。避免了描述价格动态的随机微分方程参数估计的困难问题，导出的操作程序使我们能够诊断正在形成的泡沫并预测其终止时间。在1980年2月1日至2008年10月31日期间的美国标准普尔500指数、1980年1月1日至2008年7月31日期间的美国纳斯达克综合指数和1986年12月1日至2008年11月30日期间的香港恒生指数三个金融市场进行的测试表明，泡沫预警是可行的。
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英文标题：
《Diagnostics of Rational Expectation Financial Bubbles with Stochastic
Mean-Reverting Termination Times》
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作者：
Li Lin, Didier Sornette
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最新提交年份：
2009
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to self-reinforcing transient stochastic faster-than-exponential price dynamics. As a result of the nonlinear feedbacks, the termination of a bubble is found to be characterized by a finite-time singularity in the bubble price formation process ending at some potential critical time $\tilde{t}_c$, which follows a mean-reversing stationary dynamics. Because of the heterogeneity of the rational agents' expectations, there is a synchronization problem for the optimal exit times determined by these arbitrageurs, which leads to the survival of the bubble almost all the way to its theoretical end time. The explicit exact analytical solutions of the two models provide nonlinear transformations which allow us to develop novel tests for the presence of bubbles in financial time series. Avoiding the difficult problem of parameter estimation of the stochastic differential equation describing the price dynamics, the derived operational procedures allow us to diagnose bubbles that are in the making and to forecast their termination time. The tests performed on three financial markets, the US S&P500 index from 1 February 1980 to 31 October 2008, the US NASDAQ composite index from 1 January 1980 to 31 July 2008 and the Hong Kong Hang Seng index from 1 December 1986 to 30 November 2008, suggest the feasibility of advance bubble warning.
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PDF链接：
https://arxiv.org/pdf/0911.1921
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