交易策略的资金流动与获利性演化——一个简单的市场动力学模型  

Pro tability and capital dynamics of common trading strategies in a simple nancial model

作　　者：高言 邓家品 GAO Yan;DENG Jiapin(Department of Financial Engineering,School of Finance,Central University of Finance and Economics,Beijing 100081,China;Lingnan College,Sun Yat-sen University,Guangzhou 510275,China)

机构地区：[1]中央财经大学金融学院金融工程系,北京100081 [2]中山大学岭南学院,广东广州510275

出　　处：《纯粹数学与应用数学》2023年第3期373-389,共17页Pure and Applied Mathematics

基　　金：国家自然科学基金(72002224);中央高校基本科研业务费专项基金;中央财经大学科研创新团队支持计划。

摘　　要：从实证上来看,在市场中很难找到一个长期获利的交易策略.策略的获利性随时间的演化呈现周期的状态.基于对库存风险厌恶的做市商价格形成机制,本文详细探索了两种常见策略(趋势追随策略与基本面策略)的获利性影响因素.发现资金量在限制策略的获利性和影响策略间关系上扮演了重要角色.同时,做市商对库存的风险厌恶程度也会影响策略的获利性.本文重现了实证中发现的策略获利性周期.该周期意味着一种策略的获利性是有限的,该有限性来源于该策略所吸引的资金量的增加和单位资金获利性减少之间的权衡.基于某种策略资金量的变动对另一种策略收益的影响,两两策略间的关系可以是捕食-被捕食、共生与竞争.基于策略资金的再投资机制,市场会自发地演化到两种策略收益持平的均衡状态.By empirical evidences,it is difficult to find a trading strategy with consistently good performance over a long period,and strategies′profitability seem to be varying through time in a cycle fashion.Under the price formation mechanism based on a market-maker with risk aversion to inventory,this paper elaborately detects the crucial factors that affect strategy′profitability with two common trading strategies,i.e.trend following strategy and value investing strategy.We find that the capitals invested in strategies play an important role in limiting self′s profits and affecting each other′s interactions.Also the market maker′s risk aversion to inventory could make positive or negative influences on strategies′profitability.Consistent with empirical evidences,the inverted parabola response of strategy′payoffs to self′s capitals is found.This pattern implies the profits that the strategy could bring to its users are limited and originates from the balance between the increasing capitals invested and the decreasing payoffs per capital.Based on the cross influences of the variations in one strategy′s capitals on the other′s payoffs,the interactions between the two strategies could be prey-predator,symbiosis or competition.In the long time horizon with the two strategies′payoffs reinvestment,the market can spontaneously evolve to the equilibrium where each strategy gains even.

关 键 词：稳定性分析 价格动力学 获利性周期 市场生态 

分 类 号：O186.1[理学—数学]