{"title":"技术分析的数学分析","authors":"Matthew J. Lorig, Zhou Zhou, B. Zou","doi":"10.1080/1350486X.2019.1588136","DOIUrl":null,"url":null,"abstract":"ABSTRACT In this paper, we investigate trading strategies based on exponential moving averages (ExpMAs) of an underlying risky asset. We study both logarithmic utility maximization and long-term growth rate maximization problems and find closed-form solutions when the drift of the underlying is modelled by either an Ornstein-Uhlenbeck process or a two-state continuous-time Markov chain. For the case of an Ornstein-Uhlenbeck drift, we carry out several Monte Carlo experiments in order to investigate how the performance of optimal ExpMA strategies is affected by variations in model parameters and by transaction costs.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2017-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"A Mathematical Analysis of Technical Analysis\",\"authors\":\"Matthew J. Lorig, Zhou Zhou, B. Zou\",\"doi\":\"10.1080/1350486X.2019.1588136\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"ABSTRACT In this paper, we investigate trading strategies based on exponential moving averages (ExpMAs) of an underlying risky asset. We study both logarithmic utility maximization and long-term growth rate maximization problems and find closed-form solutions when the drift of the underlying is modelled by either an Ornstein-Uhlenbeck process or a two-state continuous-time Markov chain. For the case of an Ornstein-Uhlenbeck drift, we carry out several Monte Carlo experiments in order to investigate how the performance of optimal ExpMA strategies is affected by variations in model parameters and by transaction costs.\",\"PeriodicalId\":35818,\"journal\":{\"name\":\"Applied Mathematical Finance\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematical Finance\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/1350486X.2019.1588136\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematical Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/1350486X.2019.1588136","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
ABSTRACT In this paper, we investigate trading strategies based on exponential moving averages (ExpMAs) of an underlying risky asset. We study both logarithmic utility maximization and long-term growth rate maximization problems and find closed-form solutions when the drift of the underlying is modelled by either an Ornstein-Uhlenbeck process or a two-state continuous-time Markov chain. For the case of an Ornstein-Uhlenbeck drift, we carry out several Monte Carlo experiments in order to investigate how the performance of optimal ExpMA strategies is affected by variations in model parameters and by transaction costs.
期刊介绍：
The journal encourages the confident use of applied mathematics and mathematical modelling in finance. The journal publishes papers on the following: •modelling of financial and economic primitives (interest rates, asset prices etc); •modelling market behaviour; •modelling market imperfections; •pricing of financial derivative securities; •hedging strategies; •numerical methods; •financial engineering.
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