摘要翻译：
我解开了经纪人称之为货币市场的基本长期动态，这是一堆现金，为散户客户（阅读：连续时间凯利赌徒）提供保证金贷款。赎回资金被假定为完全无弹性地供应自己，并持续地将所有本金和利息再投资。我证明了货币市场的相对规模（即相对于凯利银行的规模）是一个概率收敛到零的鞅。融资融券利率是均方收敛到抑制价格$R_\infty:=\nu-\sigma^2/2$的下鞅，其中$\nu$是股票市场的渐近复合增长率，$\sigma$是股票市场的年波动率。在这种环境下，赌徒不再是渐近A.S.战胜市场。一个指数因子（就像他在完全弹性供给下所做的那样）。相反，他以极高的概率（假设98%）通过一个因子（比如1.87,或者87%以上的最终财富）渐进地击败市场，该因子的平均值不能超过模型开始时的杠杆率（比如2:1$)。尽管赌徒的财富与同等买入并持有投资者的财富之比是一个下鞅（总是预期会增加），但他实现的复合增长率的均方收敛为$\nu$。这是因为均衡杠杆率收敛到1：1美元，与保证金贷款利率的逐步上升步调一致。
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英文标题：
《Long Run Feedback in the Broker Call Money Market》
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作者：
Alex Garivaltis
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最新提交年份：
2019
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分类信息：

一级分类：Economics        经济学
二级分类：General Economics        一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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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：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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英文摘要：
  I unravel the basic long run dynamics of the broker call money market, which is the pile of cash that funds margin loans to retail clients (read: continuous time Kelly gamblers). Call money is assumed to supply itself perfectly inelastically, and to continuously reinvest all principal and interest. I show that the relative size of the money market (that is, relative to the Kelly bankroll) is a martingale that nonetheless converges in probability to zero. The margin loan interest rate is a submartingale that converges in mean square to the choke price $r_\infty:=\nu-\sigma^2/2$, where $\nu$ is the asymptotic compound growth rate of the stock market and $\sigma$ is its annual volatility. In this environment, the gambler no longer beats the market asymptotically a.s. by an exponential factor (as he would under perfectly elastic supply). Rather, he beats the market asymptotically with very high probability (think 98%) by a factor (say 1.87, or 87% more final wealth) whose mean cannot exceed what the leverage ratio was at the start of the model (say, $2:1$). Although the ratio of the gambler's wealth to that of an equivalent buy-and-hold investor is a submartingale (always expected to increase), his realized compound growth rate converges in mean square to $\nu$. This happens because the equilibrium leverage ratio converges to $1:1$ in lockstep with the gradual rise of margin loan interest rates.
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PDF链接：
https://arxiv.org/pdf/1906.10084