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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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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中文摘要：
本文研究了一个连续时间的两人交易博弈，该博弈推广了Garivatis（2018），以考虑股票价格的跳跃和扩散。与Bell and Cover（1988）在离散时间中的做法类似，玩家首先选择初始美元的公平随机，将其交换为平均值最多为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重新平衡的投资组合中，这些投资组合必须遵守超过[0，t]$的规定。我们解决了相应的“投资$\\phi$-博弈”，即带有支付核$\\mathbb{E}[\\phi{\\textbf{W}U 1V\\U t（b）/（\\textbf{W}\\U 2V\\U t（c））\\}]$的零和博弈，其中$\\textbf{W}\\U i$是玩家i$的公平随机化，V\\U t（b）$是再平衡规则中一美元存款的最终财富，而$\\ phi（\\ bullet）$是任何用来衡量相对性能的递增函数。我们表明，唯一的鞍点是两个参与者都使用（杠杆）Kelly规则进行跳跃扩散，这通常是通过最大化渐近几乎确定的连续复合资本增长率来定义的。因此，凯利跳跃扩散规则对于任何想要（在任何时间范围内）在任何衡量相对表现的指标上胜过其他交易者的人来说，都是正确的行为。
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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：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：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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