英文标题：
《Strict Local Martingales and Optimal Investment in a Black-Scholes Model
  with a Bubble》
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作者：
Martin Herdegen, Sebastian Herrmann
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最新提交年份：
2017
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英文摘要：
  There are two major streams of literature on the modeling of financial bubbles: the strict local martingale framework and the Johansen-Ledoit-Sornette (JLS) financial bubble model. Based on a class of models that embeds the JLS model and can exhibit strict local martingale behavior, we clarify the connection between these previously disconnected approaches. While the original JLS model is never a strict local martingale, there are relaxations which can be strict local martingales and which preserve the key assumption of a log-periodic power law for the hazard rate of the time of the crash. We then study the optimal investment problem for an investor with constant relative risk aversion in this model. We show that for positive instantaneous expected returns, investors with relative risk aversion above one always ride the bubble.
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中文摘要：
关于金融泡沫建模有两大主流文献：严格局部鞅框架和约翰森·莱多伊特·索内特（JohansenLedoit-Sornette，JLS）金融泡沫模型。基于一类嵌入了JLS模型并且可以表现出严格的局部鞅行为的模型，我们阐明了这些先前断开连接的方法之间的联系。虽然原始JLS模型从来都不是严格的局部鞅，但有一些松弛可以是严格的局部鞅，并且保留了对数周期幂律对碰撞时间危险率的关键假设。在此模型中，我们研究了相对风险厌恶度为常数的投资者的最优投资问题。我们发现，对于正的瞬时预期回报，相对风险厌恶度高于1的投资者总是会在泡沫中度过难关。
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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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