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摘要翻译：
我们给出了一个乘性随机过程的分析研究，它在随机环境中模拟了一个简单的投资者动力学。投资者预算的动态性，$x(t)$，取决于投资回报的随机性，$r(t)$，对此讨论了不同的模型假设。研究了预算的胖尾分布，并与理论预测进行了比较。我们主要感兴趣的是随着时间的推移达到恒定值的预算的最有可能的值$X_MP$。基于对动力学的分析研究，我们能够预测$x_mp^stat$。我们找到了一个标度律，它将最可能值与描述随机过程的特征参数联系起来。我们的分析结果被随机计算机模拟证实，显示出非常好的符合预测。
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英文标题：
《Investments in Random Environments》
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作者：
Emeterio Navarro, Ruben Cantero, Joao Rodrigues, Frank Schweitzer
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Physics 物理学
二级分类：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, $x(t)$, depends on the stochasticity of the return on investment, $r(t)$, for which different model assumptions are discussed. The fat-tail distribution of the budget is investigated and compared with theoretical predictions. Weare mainly interested in the most probable value $x_mp$ of the budget that reaches a constant value over time. Based on an analytical investigation of the dynamics, we are able to predict $x_mp^stat$. We find a scaling law that relates the most probable value to the characteristic parameters describing the stochastic process. Our analytical results are confirmed by stochastic computer simulations that show a very good agreement with the predictions.
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PDF链接：
https://arxiv.org/pdf/0709.3630
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