英文标题：
《Long-Term Growth Rate of Expected Utility for Leveraged ETFs: Martingale
Extraction Approach》
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作者：
Tim Leung, Hyungbin Park
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最新提交年份：
2016
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英文摘要：
This paper studies the long-term growth rate of expected utility from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. Working with the power utility function, we develop an analytical approach that employs martingale extraction and involves finding the eigenpair associated with the infinitesimal generator of a Markovian time-homogeneous diffusion. We derive explicitly the long-term growth rates under a number of models for the reference asset, including the geometric Brownian motion model, GARCH model, inverse GARCH model, extended CIR model, 3/2 model, quadratic model, as well as the Heston and 3/2 stochastic volatility models. We also investigate the impact of stochastic interest rate such as the Vasicek model and the inverse GARCH short rate model. We determine the optimal leverage ratio for the long-term investor and examine the effects of model parameters.
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中文摘要：
本文研究了持有杠杆交易基金（LETF）的预期效用的长期增长率，LETF是参考资产的固定比例投资组合。利用幂效用函数，我们发展了一种分析方法，该方法采用鞅提取，并涉及到寻找与马尔可夫时间齐次扩散的无穷小生成元相关的特征对。我们明确推导了参考资产在多种模型下的长期增长率，包括几何布朗运动模型、GARCH模型、逆GARCH模型、扩展CIR模型、3/2模型、二次模型以及赫斯顿和3/2随机波动率模型。我们还研究了Vasicek模型和逆GARCH短期利率模型等随机利率的影响。我们确定了长期投资者的最佳杠杆比率，并检验了模型参数的影响。
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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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