Inefficient Bubbles and Efficient Drawdowns in Financial Markets

Mitchell T Schatz, D. Sornette
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引用次数: 13

Abstract

At odds with the common “rational expectations” framework for bubbles, economists like Hyman Minsky, Charles Kindleberger and Robert Shiller have documented that irrational behavior, ambiguous information or certain limits to arbitrage are essential drivers for bubble phenomena and financial crises. Following this understanding that asset price bubbles are generated by market failures, we present a framework for explosive semimartingales that is based on the antagonistic combination of (i) an excessive, unstable pre-crash process and (ii) a drawdown starting at some random time. This unifying framework allows one to accommodate and compare many discrete and continuous time bubble models in the literature that feature such market inefficiencies. Moreover, it significantly extends the range of feasible asset price processes during times of financial speculation and frenzy and provides a strong theoretical background for future model design in financial and risk management problem settings. This conception of bubbles also allows us to elucidate the status of rational expectation bubbles, which, by design, suffer from the paradox that a rational market should not allow for misvaluation. While the discrete time case has been extensively discussed in the literature and is most criticized for its failure to comply with rational expectations equilibria, we argue that this carries over to the finite time “strict local martingale”-approach to bubbles.
金融市场的无效泡沫和有效收缩
与常见的泡沫“理性预期”框架不同,海曼·明斯基(Hyman Minsky)、查尔斯·金德尔伯格(Charles Kindleberger)和罗伯特·希勒(Robert Shiller)等经济学家已经证明,非理性行为、模糊信息或对套利的某些限制是泡沫现象和金融危机的基本驱动因素。根据对资产价格泡沫是由市场失灵产生的理解,我们提出了一个爆炸性半鞅的框架,该框架基于(i)过度、不稳定的崩盘前过程和(ii)在某个随机时间开始的回调的对抗性组合。这个统一的框架允许人们适应和比较文献中以市场效率低下为特征的许多离散和连续时间泡沫模型。此外,它显著扩展了金融投机和狂热时期可行资产价格过程的范围,并为未来金融和风险管理问题设置的模型设计提供了强大的理论背景。泡沫的概念也使我们能够阐明理性预期泡沫的地位,理性预期泡沫在设计上受到理性市场不应允许错误估值的悖论的影响。虽然离散时间的情况已在文献中被广泛讨论,并因其未能符合理性预期均衡而受到大多数批评,但我们认为这延续到有限时间的“严格局部鞅”-泡沫方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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