摘要翻译：
托盘购买，这里的定义是投资者准备要约收购一个公司的一股股份，以获得该公司的多数股份，减少了一个投资者需要的多数股份数量。本文建立了立足点和不立足点两种策略的数学模型，并比较了两种策略下投资者的期望利润和收购公司的概率。结果表明，投资者在两种策略中的预期利润是一致的。另一方面，采用托立足点战略的公司被收购的概率要比没有托立足点战略的公司被收购的概率要高得多。在模型的分析中，我们应用了不完全贝塔函数的方法和中心二项系数的一些精化界。
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英文标题：
《Toehold Purchase Problem: A comparative analysis of two strategies》
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作者：
Iryna Banakh, Taras Banakh, Pavel Trisch and Myroslava Vovk
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最新提交年份：
2014
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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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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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英文摘要：
  Toehold purchase, defined here as purchase of one share in a firm by an investor preparing a tender offer to acquire majority of shares in it, reduces by one the number of shares this investor needs for majority. In the paper we construct mathematical models for the toehold and no-toehold strategies and compare the expected profits of the investor and the probabilities of takeover the firm in both strategies. It turns out that the expected profits of the investor in both strategies coincide. On the other hand, the probability of takeover the firm using the toehold strategy is considerably higher comparing to the no-toehold strategy. In the analysis of the models we apply the apparatus of incomplete Beta functions and some refined bounds for central binomial coefficients.
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PDF链接：
https://arxiv.org/pdf/1204.2065