跳跃扩散的博弈论最优投资组合

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摘要翻译：
本文研究了一个连续时间的两人交易博弈，该博弈推广了Garivaltis(2018)，允许股票价格既跳跃又扩散。类似于离散时间的Bell and Cover(1988)，参与者首先选择初始美元的公平随机化，将其交换为平均数至多为1的随机财富。然后，每个参与者将产生的资本存入一些持续再平衡的投资组合，这些投资组合必须坚持超过[0,t]$。我们求解相应的'investment$\phi$-game'，即具有支付内核的零和博弈$\mathbb{E}[\phi\{\textbf{W}_1v_t(b)/(\textbf{W}_2v_t(c))\}]$，其中$\textbf{W}_i$是玩家$i$的公平随机化，$v_t(b)$是在再平衡规则$b$中积累的一美元存款的最终财富，$\phi(\bulle)$是任何用于衡量相对性能的递增函数。我们证明了唯一的鞍点是两个参与者使用跳跃扩散的（杠杆）凯利规则，该规则通常是通过最大化渐近几乎肯定的连续复合资本增长率来定义的。因此，凯利规则的跳跃扩散是正确的行为，对于任何人谁想要胜过其他交易者（在任何时间框架内），实际上任何衡量相对表现的措施。
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英文标题：
《Game-Theoretic Optimal Portfolios for Jump Diffusions》
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作者：
Alex Garivaltis
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最新提交年份：
2018
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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。
--
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
--
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：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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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：
  This paper studies a two-person trading game in continuous time that generalizes Garivaltis (2018) to allow for stock prices that both jump and diffuse. Analogous to Bell and Cover (1988) in discrete time, the players start by choosing fair randomizations of the initial dollar, by exchanging it for a random wealth whose mean is at most 1. Each player then deposits the resulting capital into some continuously-rebalanced portfolio that must be adhered to over $[0,t]$. We solve the corresponding `investment $\phi$-game,' namely the zero-sum game with payoff kernel $\mathbb{E}[\phi\{\textbf{W}_1V_t(b)/(\textbf{W}_2V_t(c))\}]$, where $\textbf{W}_i$ is player $i$'s fair randomization, $V_t(b)$ is the final wealth that accrues to a one dollar deposit into the rebalancing rule $b$, and $\phi(\bullet)$ is any increasing function meant to measure relative performance. We show that the unique saddle point is for both players to use the (leveraged) Kelly rule for jump diffusions, which is ordinarily defined by maximizing the asymptotic almost-sure continuously-compounded capital growth rate. Thus, the Kelly rule for jump diffusions is the correct behavior for practically anybody who wants to outperform other traders (on any time frame) with respect to practically any measure of relative performance.
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PDF链接：
https://arxiv.org/pdf/1812.04603

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关键词：投资组合 博弈论 Quantitative Contribution Mathematical both 资本 rule game 性能