安徽大学硕士学位论文基于区间数的证券投资组合模型和实证研究姓名：刘亭亭申请学位级别：硕士专业：技术经济及管理指导教师：陈华友2010-04
摘 要 本文在相关文献研究的基础上建立了一种预期收益率和风险损失率均为区间数的证券投资组合模型，并且通过引入风险偏好系数α和目标函数优化水平参数β的方法，将基于区间数的多目标线性规划模型进行简化。投资者可以根据自己对风险的喜好程度和对投资市场的走势的乐观估计程度来选取参数α和β，增加了决策的柔性，也考虑到了投资者的心理，并依据我国上海股票交易所的20支上市股票给出了实证分析的过程，选取了指数平滑法利用20支股票52周的周收益率来确定预期收益率的区间值，建立多目标区间数线性规划模型求解得出资产组合的最优配置，文章的最后探讨了模型在中国投资市场的实用性问题。 主要工作概括如下： 第一章首先根据中国证券市场的发展现状以及证券投资理论、模糊决策理论的发展现状阐述了论文的研究背景与研究意义，总结了近年来国内外证券投资组合决策理论、模型和算法的研究成果。 第二章针对文章涉及的主要理论进行了综述，包括基于模糊意义下的证券投资组合模型、现代决策理论中的多属性决策和多目标决策的理论和方法、区间数理论和单项预测方法，对于以上理论的相关概念给出了阐述。 第三章在Markowitz均值-方差模型的理论基础上讨论了引入区间数的证券投资组合模型，并给出一种区间模糊数证券投资组合线性规划模型，通过引入风险偏好系数α，目标函数优化水平参数β的方法将模型转化为一般参数线性规划进行求解。 第四章给出了模型的实证分析，在数据处理的过程中采用了指数平滑预测的方法来求取区间数证券投资组合的预期收益率的区间数，最后给出模型求解结果，验证了模型的有效性。 第五章给出了总结和不足，并对未来的研究前景作了展望。 关键词：证券投资组合；区间数；线性规划；预期收益率 I
Abstract This dissertation established a rate of return and risk expected loss rate of interval fuzzy number of the securities portfolio model which based on literature studies，through the introduction of risk factorα and objective function optimization level parameterβto simplify the interval-based multi-objective linear programming model . Investors can estimate model to select the parameter according to which degree of risk preferences and investment trend of the market's optimism. This model increases flexibility in decision-making, but the psychology of investors is also taken into account. Finally, according to Chinese Shanghai Stock Exchange's 20 listed stocks, the model is given the empirical results. Dissertation selected the exponential and smoothing method using 20 stocks' week rates of the 52 weeks to determine the expected rate of return interval values and used a multi-objective fuzzy interval number linear programming model to derive the optimal portfolio allocation. Afterwards, I discuss the model in question of the practicality of the Chinese investment market. The main works is summarized as follows: In the first chapter it firstly introduced the development of Chinese securities market, the concept of securities and investment theory and the development of the theory of fuzzy decision, which is base on these situations to described the dissertation’s research background and research significance, and summarized domestic and foreign portfolio decision theories, models and algorithms of major research achievements. The second chapter reviewed and explained the main theories for the article, including a fuzzy-based portfolio model, modern decision theory of multi-attribute decision-making and of multi-objective decision theory and method, interval number theory and single forecast methods. The third chapter introduced interval number of the securities portfolio model based on the Markowitz M-V model theory, and gave kind of interval fuzzy number II
linear programming model portfolio. Then, the interval number of the securities portfolio model is converted into the general linear programming by introducing the coefficient of risk preferences and the level of objective function optimization method of the model parameters. The fourth chapter made the model analysis. The data processing using exponential smoothing forecast is a more scientific method to obtain the expected return rate of interval fuzzy numbers. In addition, the chapter solved the model results are given to prove the validity of the model. The fifth chapter summed up full text job, and described the text's weaknesses and future research prospects. Key words: Portfolio investment: Interval number; Linear programming; Expected rate of return. III
独创性声明 本人声明所呈交的学位论文是本人在导师指导下进行的研究工作及取得的研究成果。据我所知，除了文中特别加以标注和致谢的地方外，论文中不包含其他人已经发表或撰写过的研究成果，也不包含为获得 或其他教育机构的学位或证书而使用过的材料。与我一同工作的同志对本研究所做的任何贡献均已在论文中作了明确的说明并表示谢意。 学位论文作者签名： 签字日期： 年 月 日 学位论文版权使用授权书 本学位论文作者完全了解 有关保留、使用学位论文的规定，有权保留并向国家有关部门或机构送交论文的复印件和磁盘，允许论文被查阅和借阅。本人授权 可以将学位论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存、汇编学位论文。 （保密的学位论文在解密后适用本授权书） 学位论文作者签名： 导师签名： 签字日期： 年 月 日 签字日期： 年 月 日 学位论文作者毕业去向： 工作单位： 电话： 通讯地址： 邮编：
뗚튻헂 탷 싛 뗚튻헂 탷 싛 20쫀볍80쓪듺틔살ꎬ좫쟲뷰죚탐튵톸쏍랢햹ꎬ뷰죚좫쟲뮯뷸돌볓뿬볓뻧ꎬ뷰죚탐튵뗄뺺헹튲쯦횮볓뻧ꎬ틲뛸룷훖뷰죚퇜짺닺욷늻뛏펿쿖ꎬ뷰죚믮뚯뛔컒쏇죕뎣짺믮뗄펰쿬튲죕틦볓뻧ꆣ뷰죚쫐뎡뿉틔ퟔ랢뗄뗷뷚짺닺풴뗄엤훃ꎬ쯹틔쓜퓚죋샠뺭볃믮뚯훐냧퇝훘튪뷇즫ꎬ떫쫇춬쪱ꎬ컒쏇뇘탫돐떣룷훖뷰죚춶믮뚯듸살뗄럧쿕ꆣ1992쓪뗄얷훞믵뇒쳥쾵캣믺ꎬ1997쓪뗄퇇훞뷰죚캣믺ꎬ2007-2008쓪평듎듻캣믺틽랢뗄뮷쟲뷰죚캣믺ꎬ뚼늨벰떽뫜뛠믺릹ꆢ뗘쟸뫍맺볒ꎬ떼훂뫜뛠믺릹떹뇕ꎬ웤훐튲냼삨튻킩뷏듳뷏캪횪쏻뗄웳튵ꎬ짵훁쪹맺볒믲헟뗘쟸뗄뺭볃쿝죫캣믺ꎬ뇈죧뇹떺뗄뺭볃캣믺ꆣ 죋쏇쏦뛔뷰죚쫐뎡뗄늻뛏뾪럅뒴탂뇤뮯ꎬ쇋뷢죏쪶쇋뷰죚쫐뎡ꎬ튲쇋뷢떽춶믮뚯뗄럧쿕ꎬ뺡솿뗄복킡춶럧쿕늢쟒믱뗃뷏듳샻틦ꎬ돉캪춶헟뇘탫뾼싇튲쫇훘뗣뾼싇뗄컊쳢ꆣ톧쫵뫍쿖쪵ퟜ쫇쾢쾢쿠맘뗄ꎬ뷰죚ퟩ뫏풤닢쒣탍뗄퇐뺿튲쯦헟춶죈돉캪죈뗣ꆣ뷰죚닺뗄춶럧쿕듳킡죧뫎좷뚨ꎬ뷰죚닺뗄쫕틦ꆢ럧쿕틔벰쇷뚯탔컊쳢횮볤듦퓚쎬뛜ꎬ춶헟죧뫎좨뫢ꎬ뚼쫇맘힢뗄붹뗣컊쳢ꎬ튲쫇춶뻶닟뗄뫋탄컊쳢ꆣ뛸춶헟퓚싺ퟣퟔ벺뗄룶죋욫뫃쳵볾쿂퓵퇹뛔쫕틦뫍럧쿕뗄뷸탐좨뫢뫍폅뮯ꎬ튲쫇퇐뺿뗄죈뗣컊쳢횮튻ꆣ 튻ꆢ퇐뺿놳뺰 훚쯹훜횪ꎬퟩ뫏풤닢튻냣쫇퓚늻좷뚨뗄뮷뺳훐뷸탐뗄ꎬ뛸쟒헢룶뮷뺳뮹춨뎣퓚튻뚨뗄쪱볤뛎쓚늻뛏뇤뮻ꆣ룷훖틲쯘뗄늻좷뚨벰늻컈뚨ꎬ뚼믡떼훂풤닢쒣탍뗄늻좷뚨뫍풤닢뗄럧쿕ꎬ쳘뇰쫇짦벰떽횤좯춶컊쳢쪱ꆣ횤좯춶ퟩ뫏 (Portfolio)쫇평룶죋믲믺릹돖폐뗄룷훖횤좯(죧막욱ꆢ햮좯ꆢ늻뚯닺춶ꆢ쿖뷰뗈볛컯믲웤쯻닺뗈)릹돉뗄닺ꆣ횤좯춶헟죧맻냑뷰럖즢뗘춶퓚벸[1]훖횤좯짏ꎬ뿉틔럖즢복짙춶럧쿕ꆣ 횤좯춶ퟩ뫏뗄몭틥쫇횸춶헟룹뻝럧쿕횤좯뗄럧쿕듳킡뫍쫕틦싊ꎬ내헕튻뚨뗄풭퓲뷸탐뛔쯹톡막욱뷸탐ퟩ뫏ꎬ웤훐ꎬ쫕틦뫍럧쿕쫇횤좯춶뗄솽룶맘볼뗄뫋탄컊쳢ꆣ퓚횤좯춶뗄맽돌훐ꎬ춶헟ퟜ쫇ힷ쟳쫕틦뗄ퟮ듳뮯뫍럧쿕뗄ퟮ킡뮯ꎬ떫쫇훚쯹훜횪ꎬ럧쿕쫇쫕틦뗄늹뎥ꎬ퓵퇹퓚럧쿕뺡뿉쓜킡뗄쟩뿶쿂믱뗃뷏듳쫕틦ꎬ1
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 듓훐톰헒떽튻훖뻹뫢ꎬ헽쫇퇐뺿뗄훘뗣ꆣ횤좯춶ퟩ뫏샭싛뿉틔쮵쫇뷰죚톧훐랢햹ퟮ캪톸쯙ꆢ펦폃ퟮ캪맣랺뗄쇬폲횮튻ꆣ 퓚쿖쪵훐ꎬ횤좯춶쫐뎡쫇튻룶벫웤뢴퓓뗄쾵춳ꎬ쯼뗄뷰죚닺뗄쫕틦ꆢ럧쿕틔벰쇷뚯탔뗈뫜뛠틲쯘뚼쫇늻좷뚨뗄ꎬ헢뻍쪹뗃춶헟탨튪퓚튻룶늻좷뚨뗄뮷뺳쿂ퟶ돶춶뻶닟ꆣ뿉틔쮵ꎬ튪ퟶ돶헽좷뗄뻶닟뗄잰쳡쫗쿈뻍쫇쓜헽좷뗘죏쪶떽횤좯쫐뎡룷훖틲쯘뗄늻좷뚨탔ꎬ춬퇹ꎬ뿍맛뗘쏨쫶늻좷뚨탔튲쫇뿉틔뇜쏢평폚늻좷뚨탔듸살뗄쯰쪧뗄ꆣ뛸퓚뺭볃풤닢쇬폲뗄퇐뺿훐ꎬ튻룶쿔훸쳘뗣뻍쫇뺡솿붨솢쳹뷼쿖쪵뗄쒣탍ꎬ뛸쿖쪵훐뗄쟩뿶폖뻟폐쒣뫽탔튲벴늻좷뚨탔ꎬ뇈죧춶헟퓚춶쪱ꎬ뿉틔돐떣뗄럧쿕뫍웚췻뗄쫕틦웤쪵뚼쫇퓚쒳튻랶캧쓚ꎬ폚쫇틽죫쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍뻍쿔뗃룼볓쳹뷼쪵볊ꆣ퓚헢샯ꎬ럧쿕뫍쫕틦뚼틔쟸볤쫽뗄탎쪽돶쿖ꎬ룼쟐뫏춶쫐뎡뗄늻좷뚨쳘헷뫍춶헟뗄쪵볊탄샭쟩뿶ꆣ 뛾ꆢ퇐뺿틢틥 억놴뛻붱뗃훷쳡돶쇋횤좯ퟩ뫏춶뻹횵-랽닮쒣탍ꎬ헢튻[1]쒣탍놻죏캪쫇쿖듺횤좯ퟩ뫏춶샭싛뗄믹쪯ꆣ1952쓪ꎬMarkowitz뗄싛컄ꆶ[2]닺톡퓱ꆷ랢뇭ꎬ뫳폖폚1959쓪돶냦쇋ꆶ닺ퟩ뫏톡퓱ꎺ춶뗄폐킧럖즢뮯ꆷꎬ쪹뗃춶럧쿕쫗듎퓚톧쫵짏놻솿뮯ꎬ뾪뒴쇋뚨솿뮯퇐뺿춶ퟩ뫏뗄쿈뫓ꆣ춶ퟩ뫏톡퓱뗄몭틥뻍쫇퓚럻뫏춶헟뛔럧쿕ꆢ쫕틦틔벰쇷뚯탔쟩뿶뗄좨뫢쿂엤훃룷훖뷰죚닺쓜쪹춷듧ퟮ뫃ꎬퟔ듋ꎬ뷰죚톧뾪쪼뷸죫떽훰늽뒿샭싛퇐뺿뫍뺭퇩횸떼뗄ힴ첬ꆣ횮뫳ꎬ맺쓚췢탭뛠톧헟훂솦폚헢랽쏦뗄퇐뺿ꎬ늢쟒좡뗃쇋탭뛠럡쮶뗄돉맻ꆣ[3][4]Sharp뫍lintner뗈퓚Markowitz쳡돶뻹횵-랽닮횤좯ퟩ뫏톡퓱쒣탍뗄믹뒡짏쳡돶쇋놾닺뚨볛쒣탍ꎨCAPMꎩ,뛔횤좯쫐뎡뻹뫢쪱뗄횤좯쫐뎡볛룱탐캪뷸탐퇐뺿ꆣ[5]퓚쯻뗄ꆶ놾닺뚨볛——쳗샻뚨볛샭싛ꆷ튻컄훐횸돶ꎬ죎뫎닺뗄볛룱뿉틔뇭쪾캪튻킩“릲춬틲쯘”뗄쿟탔ퟩ뫏ꎬ벴놾쫐뎡훐쒳훖닺뗄볛룱뿉틔샻폃놾쫐뎡틔췢뗄웤쯻틲쯘쯹좷뚨,쳡돶쇋쳗샻뚨볛샭싛ꎨAPTꎩꆣ헢죽늿럖돉캪쿖듺뷰죚샭싛뗄훘튪ퟩ돉늿럖ꆣ좻뛸쿖쪵훐헦쪵뗄쟩뿶튪뢴퓓뫜뛠ꆣ뷰죚쫐뎡ퟮ듳뗄쳘뗣뻍쫇늻좷뚨탔ꎬ폐톧헟죏캪틲캪늻좷뚨탔컞램뷸탐풤닢ꎬ듓뛸볓짮쇋횤좯쫐뎡뗄럧쿕ꆣ쯹틔퓸뺭튻뛎쪱볤쓚ꎬ늻좷뚨탔뗈폚럧쿕ꎬ뛸폖틲캪늻좷뚨탔쫇틲캪룷훖틲쯘뻟폐쯦믺탔퓬돉뗄ꎬ쯹틔럧쿕뗈춬폚쯦믺탔ꆣ떫쫇뫳살춨맽2
뗚튻헂 탷 싛 퇐뺿폖랢쿖헢퇹늢컞램뛔횤좯춶뷸탐헦헽뗄횸떼ꎬ뛸횤좯쫐뎡뗄뫜뛠뇤뮯늢늻쓜폃쯦믺살쏨쫶ꆣ폚쫇헫뛔횤좯쫐뎡늻좷뚨탔ꎬ퓵퇹뷸탐ퟩ뫏춶뗄뻶닟ꎬ돉쇋횤좯ퟩ뫏춶샭싛퇐뺿뗄튻룶훘튪랽쿲ꆣ 쯦ퟅ뷼쓪살늻좷뚨쟩뿶쿂뗄뻶닟컊쳢퇐뺿뗄랢햹ꎬ늻좷뚨뛠쫴탔뻶닟놻펦폃떽랽랽쏦쏦뗄퇐뺿훐좥ꆣ뛸헢훖늻좷뚨뛠쫴탔뗄뻶닟폖잡잡룺춶헟튪쟳믘놨죡탔뮯쿠쟐뫏ꆣ튲뻍쫇쮵춶헟퓚춶뗄쟩뿶쿂튪쟳뗄믘놨싊뫍쓜릻돐떱뗄럧쿕뚼[6]쫇퓚튻뚨랶캧쓚뗄ꆣ슷펦뷰ꎬ쳆킡컒ꎬ훜ퟚ럅2004쓪2퓂폚쾵춳릤돌톧놨짏랢뇭싛컄ꆶ횤좯ퟩ뫏춶뗄쟸볤쫽쿟탔맦뮮랽램ꆷꎬ춨맽붫쟸볤쫽틽죫횤좯ퟩ뫏춶맦뮮뗄랽램ꎬ붫쫕틦늨뚯뫍럧쿕쯰쪧싊뚼틔쟸볤쫽뗄탎쪽뇭쪾돶살ꎬ좻뫳춨맽틽죫뫢솿춶헟럧쿕쾲뫃뗄럧쿕욫뫃쾵쫽αꎬ붫쟸볤쫽쿟탔맦뮮컊쳢뮯캪닎쫽쿟탔맦뮮컊쳢ꎬ듓뛸퓚쪹쒣탍룼뷓뷼쪵볊뗄잰쳡쿂튲쳡릩쇋튻훖뷏캪볲떥뗄뷢램ꆣ 퓚훐맺ꎬ컒쏇횤좯춶쫐뎡평폚웰늽췭ꎬ폫췢맺닮뻠뫜듳ꎬ럖즢춶뗄쮼쿫룕놻웕춨춶헟뷓쫜ꎬ샭닆뗄쮼쿫뮹늻짮죫죋탄ꆣ톧헟퓚헢랽쏦뗄퇐뺿튲실뫳췢맺뫜뛠쓪ꎬ떫쫇뷼쓪살ꎬ쯦ퟅ컒맺횤좯쫐뎡뗄뷸튻늽랢햹ꎬ컒쏇뗄샭싛퇐뺿튲풽살풽쟐뫏쪵볊ꆣ쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍뗄짮죫퇐뺿뫍랢햹ꎬ룼쳹뫏쪵볊쟩뿶ꎬ룼뻟폐죡탔ꎬ뛔춶헟뗄춶샭닆뿉틔웰떽뫜뫃뗄풤닢닎뾼ퟷ폃ꆣ 죽ꆢ맺쓚췢퇐뺿쿖ힴ ꎨ튻ꎩ맺쓚췢퇐뺿쟷쫆 뷼킩쓪살ꎬ맺췢톧헟훷튪벯훐퓚믹폚쪵볊쟩뿶쿂펦폃뗄믹뒡짏뛔춶쒣탍뷸[1]탐쿠맘뗄룄뷸뒴탂ꆣ훷튪벯훐퓚틔쿂벸룶랽쏦ꎺ 1ꆢ첽쳖탂뗄럧쿕뛈솿뇪ힼ뫍탂뗄춶ힼ퓲컊쳢ꆣ 2ꆢ듳맦쒣횤좯ퟩ뫏춶탎돉뗄듳탍뻘헳뗄폐킧쯣램컊쳢ꆣ 3ꆢ퇐뺿맘폚럅뿭M-V쒣탍뗄볙짨쳵볾믲헟퓚퓶볓웤쯻풼쫸쳵볾쿂뗄춶뻶닟컊쳢ꆣ 4ꆢ붫떥훜웚춶ퟩ뫏샭싛췆맣떽뛠웚ꎬ퇐뺿뛠웚뚯첬춶ퟩ뫏컊쳢ꆣ 5ꆢ늻췪좫탅쾢뮷뺳쿂ퟩ뫏춶쒣탍뗄붨솢뫍퇐뺿컊쳢ꆣ [6]뷼쓪살춶ퟩ뫏뻟폐듺뇭탔뗄퇐뺿돉맻훷튪폐: 틔뻹횵ꆪ랽닮춶뻶닟3
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 쒣탍캪믹뒡룄뷸뗄횤좯춶ퟩ뫏쒣탍뗄쿟탔맦뮮랽램ꎬ뛾듎맦뮮ퟩ뫏춶뻶닟랽램ꎬ펦폃쒣뫽맦뮮랽램뫍쯦믺ퟮ폅뿘훆랽램뗄횤좯춶뚯첬뿘훆랽램ꎬ틔룄뷸횤좯럧쿕뛈솿뗄랽램ퟅ쫖뗄횤좯ퟩ뫏춶컊쳢뗄룄뷸쒣탍뗈뗈ꆣ 퓚쿖쪵횤좯쫐뎡훐, 럧쿕횤좯뗄쫕틦뫍럧쿕믡틲캪횤좯쫐뎡뗄룷훖틲쯘뇤뚯뗄펰쿬ꎬ틲뛸쫇튻룶뚯첬늨뚯횵, 틲듋죧맻붫럧쿕횤좯뗄풤웚쫕틦싊뫍럧쿕쯰쪧싊뒦샭돉늻좷뚨뗄쒣뫽쟸볤쫽, 붫믡룼뷓뷼쿖쪵횤좯쫐뎡ꎬ튲믡뷸튻늽쳡룟뻶닟뗄죡탔. 뛸닉폃쇋쟸볤쫽쿟탔맦뮮랽램살퇐뺿횤좯ퟩ뫏춶컊쳢ꎬ볈쫇뷼쓪살뗄튻룶퇐뺿죈뗣ꎬ튲폐뷏잿뗄쿖쪵틢틥ꆣ믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍퓚훐맺횤좯쫐뎡뗄펦폃뫍쿖쪵틢틥튲헽쫇놾컄튪첽쳖뗄컊쳢ꆣ ꎨ뛾ꎩ맺췢퇐뺿쿖ힴ 춶ퟩ뫏샭싛ꎨModern Portfolio Theoryꎩ놻죏캪쫇쿖듺뷰죚샭싛뗄뫋탄ꎬ춶ퟩ뫏샭싛뗄믹놾쮼슷쫇춨맽럖즢뮯뗄춶뗄랽쪽살뛔돥튻늿럖뗄춶럧쿕ꎬ웤훷튪쓚죝뻍쫇퇐뺿퓵퇹퓚캴살뷡맻늻좷뚨뗄쟩뿶쿂뛔폐쿞뗄닺뷸탐춶틔쪹뗃쫕틦ퟮ듳뮯뫍럧쿕ퟮ킡뮯ꆣ쫕틦폫럧쿕좨뫢뗄폅뮯쒿뇪쫇퓚춶헟뿉틔뷓쫜뗄럧쿕돌뛈쿂쪹풤웚쫕틦듯떽ퟮ듳ꎬ믲헟쓜퓚춶헟쓜릻뷓쫜뗄풤웚쫕틦뗄쮮욽쿂쓜쪹럧쿕듯떽ퟮ킡ꆣ 쿖듺춶ퟩ뫏샭싛튻횱놻죏캪쫇컷랽쿖듺춶샭싛뗄뫋탄ퟩ돉늿럖횮튻ꎬ튲쫇뷼쓪살뷰죚닆컱뗈쇬폲맣랺맘힢뗄뫍짮죫첽쳖뗄훘뗣죈뗣뿎쳢ꆣ듋샭싛틔닺뗄쫕틦뫍럧쿕볤뗄쿠뮥맘쾵ퟷ캪퇐뺿뗄돶랢뗣뫍튪뗣ꎬ춨맽샭싛돩쿳ꎬ춳볆톧ꎬ펦폃쫽톧뗈튻킩랽램ꎬ뛔닺ퟩ뫏뗄쳘탔쳘헷뷸탐틔뚨솿캪훷뗄럖컶퇐뺿ꆣ 1ꆢM-V쒣탍 [2]1952쓪ꎬ쏀맺뺭볃톧볒ꎬ뷰죚톧볒Harry .랢뇭쇋ꆶ횤좯ퟩ뫏톡퓱ꆷ뗄싛컄ꎬ늢틲듋믱뗃쇋억놴뛻뺭볃톧붱ꆣ퓚듋싛컄훐ꎬMarkowitz냑횤좯ퟩ뫏럧쿕뫍쫕틦횮볤뗄쳦듺맘쾵뷸탐쇋쫽솿뮯ꎬ뛸뫳쳡돶쇋뻹뫢럖컶뗄탂쮼슷뫍럖컶랽램ꆣ헢뻍쫇쿖듺횤좯ퟩ뫏샭싛(Modern Portfolio Theory)뗄믹놾뿲볜ꆣMarkowitz쳡돶냑횤좯쫕틦싊짨캪튻룶쯦믺뇤솿ꎬ냑쯦믺뇤솿뗄웚췻짨캪캴살쫕틦ꎬ폃횤좯쫕틦싊뗄랽닮믲헟쮵뇪ힼ닮살뛈솿춶럧쿕ꎬ헢뻍쫇컒쏇돆횮캪뻹횵-랽닮쒣탍뗄M-V쒣탍ꆣ M-V쒣탍짨뚨쇋튻킩춶헟탐캪뗄볙짨:뇈죧춶헟뿉톡퓱뗄쎿튻훖춶뚼4
뗚튻헂 탷 싛 쫇뿉틔폃튻룶돖폐웚뗄풤웚쫕틦뗄룅싊럖늼살뇭쪾ꎻ춶헟뗄춶킧폃쟺쿟뗄뇟뷧킧폃쫇뗝복뗄ꎻ춶헟횻쓜룹뻝풤웚쫕틦뫍럧쿕살ퟶ돶춶뻶뚨ꎬ헢킩뚼쫇폫쿖쪵훐뗄쟩뿶늻럻뗄ꆣ폈웤쫇떱톡퓱뷏뛠횤좯욷훖쪱ꎬ룃쒣탍뇤돉튻룶듳탍돭쏜킭랽닮뻘헳뗄뛾듎맦뮮컊쳢ꎬ룸쟳뷢듸살튻뚨뗄삧쓑ꆣ 헫뛔M-V쒣탍뗄훖훖늻ퟣꎬ뫜뛠톧헟룸돶쇋룄뷸쒣탍ꆣ [7] Mao뗈퓚1970쓪쳡돶쇋M-V쒣탍뗄룄뷸쒣탍뻹횵ꎭ냫랽닮춶ퟩ뫏쒣탍ꎬ룃쒣탍쫇퓚볙짨춶헟횻맘탄뗍폚웚췻쫕틦뗄쓇늿럖럧쿕뗄잰쳡쿂붨솢뗄ꆣ[8]Konno 폚1990쓪쳡돶쇋뻹횵ꎭ뻸뛔욫닮춶ퟩ뫏쒣탍ꎬ헢룶쒣탍쫇폃춶ퟩ뫏캴살쫕틦뗍폚웚췻쫕틦뛸탎돉뗄뻸뛔욫닮살ퟷ캪춶럧쿕뗄뛈솿ꎬ헢룶쒣탍붫룼뛠뗄힢틢솦럅퓚뿘훆춶럧쿕짏ꎬ떫쫇폫M-V쒣탍춬퇹뻟폐늻쓜헽좷랴펳춶헟욫뫃뗈쿖쪵컊쳢ꆣ뇈죧Markowitz뗄M-V쒣탍쫇퓚늻퓊탭싴뿕뗄쿞훆쳵볾쿂ꎬ헢쫇탂탋횤좯쫐뎡뗄쳘헷ꎬ떫쫇퓚랢듯뗄횤좯쫐뎡짏ꎬ쿞훆탔싴뿕쫇듦퓚늢놻퓊[9]탭뗄ꆣAlexander퓚1993쓪쫗듎쳡돶쇋쿞훆탔싴뿕뗄쒣탍ꎬ늢쟒쳖싛쇋떥횸쫽쫕틦싊쒣탍쿂폐킧ퟩ뫏뗄좷뚨랽램ꎬ떫쫇싛컄훐늢쎻폐쳡벰튻냣쟩뿶쿂뗄폐킧뇟[10]뷧뫍폐킧뗄횤좯ퟩ뫏쳘헷뗈쓚죝ꆣ2000쓪Xia Yuesen 쳡돶쇋듸탲웚췻쫕틦뗄ퟩ뫏춶쒣탍ꎬ늢퓚쒣탍뗄볆쯣훐룸돶쇋틅뒫쯣램폃틔뷢뻶듳맦쒣횤좯ퟩ뫏춶[11]쒣탍뗄볆쯣삧쓑뗄컊쳢ꆣ춬퇹쫇2000쓪ꎬLi Zhongfei뗈룹뻝횤좯쫐뎡붻틗쪵볊듦퓚붻틗럑뗄쟩뿶퇐뺿쇋듸폐붻틗럑폃뗄뻹횵-랽닮쒣탍늢룸돶쇋쿟탔맦뮮뗄[12]볆쯣랽램ꆣ2002쓪ꎬKonno폖쳡돶쇋튻훖탂뗄뻹횵-랽닮쒣탍뗄뒦샭랽램ꎬ춨맽뷡뫏틲ퟓ쒣탍뫍쿟탔맦뮮쒣탍뗄랽쪽뿉폐킧뗘뒦샭듳맦쒣춶ퟩ뫏컊쳢ꎬ뫜뫃뗄뷢뻶쇋듳맦쒣춶ퟩ뫏쒣탍볆쯣뒦샭삧쓑뗄컊쳢ꆣ 2ꆢ놾닺뚨볛ꎨCAPMꎩ쒣탍 [3]1964쓪ꎬ쏀맺뺭볃톧볒ꆢ억놴뛻붱뷰믱뗃헟랢뇭쇋ꆶ놾닺뚨볛:럧쿕쳵볾쿂뗄쫐뎡뻹뫢샭싛ꆷꆣ1965쓪ꎬ쏀맺뺭볃톧볒ꆢ억놴뛻붱[4]뷰믱뗃헟John Lintner뗄컄헂ꆶ럧쿕닺뗄볛횵ꎬ막욱닺ퟩ뫏뗄럧쿕춶톡퓱ꎬ놾풤쯣ꆷꆣ퓚룸돶쇋뇈뷏잿뗄볙짨쳵볾횮쿂ꎬ룸돶쇋놾닺뚨볛쒣탍ꎨCapital Asset Pricing Modelꎬ볲돆CAPMꎩꆣCAPM쒣탍훷튪쫇춨맽쏨쫶횤좯뗄럧쿕볛룱뷸뛸뗃돶쫐뎡뻹뫢볛룱뗄탎돉믺샭뗄ꆣ춬쪱ꎬSharp뮹쳡돶쇋β쾵쫽뗄룅쓮ꎬ헢쫇튻룶쒣탍훐볆솿럧쿕뗄훘튪뗄횸뇪ꎬ퓚횮뫳뫜뛠횤좯ퟩ뫏춶럧쿕뗄퇐뺿훐뚼5
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 퓸돶쿖폃살뫢솿쒣탍뗄럧쿕ꆣ 톧헟쏇웕뇩죏캪CAPM쒣탍쫇뛔M-V쒣탍뗄볲뮯ꆣCAPM퓚볙짨룷룶횤좯볤쫇늻쿠맘늢쟒횤좯뗄쫕틦싊횻쓜폫쫐뎡틲쯘폐맘뗄잰쳡쿂ꎬ폃뛔뷇쿟쒣탍쪽볲뮯쇋M-V뻘헳훐뗄럇뛔뷇쿟풪쯘ꎬ쪹M-V뻘헳뗄볆쯣듳듳볲뮯ꆣ떫쫇듋쒣탍튲듦퓚뫜듳뗄늻ퟣꎬ뇈죧쒣탍볙짨횤좯뗄쫕틦싊횻폫쫐뎡틲쯘폐맘ꎬ헢킩쫐뎡펰쿬틲쯘뗄뷧뚨뻍럇뎣뗄뢴퓓ꎬ뫢솿룼쫇뢴퓓ꆣ뛸쟒CAPM쒣탍뗄춶럧쿕틀좻닉폃룺M-V쒣탍튻퇹뗄랽닮뫍킭랽닮살볆쯣ꎬ헢뻍튲뻟폐뫍M-V쒣탍튻퇹뗄좱쿝ꎬ벴랽닮늢늻쓜췪좫뗄랴펦럧쿕뗄컊쳢ꆣ쇭췢ꎬ쒣탍튪쟳횤좯쫐뎡뗄β쾵쫽폫웚췻쫕틦횮볤싺ퟣ듦퓚헽쿟탔맘쾵,헢뻍틢캶ퟅ튪쟳쫐뎡횸쫽캻폚M-V쒣탍뗄폐킧뇟뷧짏.떫쫇퓚쿖쪵뢴퓓뗄횤좯쫐뎡ꎬ헢튻뗣쫇뫜쓑싺ퟣ뫍쪵쿖뗄ꆣ [13]Black(1972)쳡돶쇋쇣놴쯾놾닺뚨볛쒣탍ꎬ퓚듋쒣탍훐ꎬ럅쯉쇋Sharp뫍Lintner뗄CAPM쒣탍훐맘폚듦퓚컞럧쿕닺뗄볙짨쳵볾ꎬ뛸쫇폫쫐뎡ퟩ뫏쫕틦늻쿠맘뗄횤좯ퟩ뫏ꎬ틲듋β캪쇣ꎬ맊돆캪쇣놴쯾횤좯ퟩ뫏ꆣ헢룶쒣탍쫇뛔듦퓚컞럧쿕닺뗄CAPM뗄튻룶룄뷸ꎬ떫쫇늢늻뻟폐뫜듳뗄쿖쪵틢틥ꆣ [14]Fama퓚웤1970쓪랢뇭뗄싛컄훐횸돶ꎬ떥뷗뛎뗄CAPM쒣탍뿉틔삩햹돉 [15]뛠웚ꎬ벴춶헟퓚뛠룶뷗뛎쫇퓚늻뛏뷸탐춶탐캪뗄ꆣ1973쓪Merton쓪쳡돶쇋ICAPMꎨInternational Capital Asset Pricing Modelꎩ쒣탍ꎬ쯤좻헢룶쒣탍늢쎻폐냑떥뷗뛎뗄CAPM쒣탍삩햹떽뛠뷗뛎ꎬ떫쫇헢룶쒣탍쳥쿖돶튻훖쮼쿫ꎬ뻍쫇춶헟퓚뾼싇춶킧폃ퟮ듳뮯쪱ꎬ늢늻뷶뷶횻뾼싇쿖퓚헢룶쪱웚ꎬ뮹뿉쓜뾼싇쿂튻룶춶쪱웚쓚뗄뿉쓜쫕틦ꎬ튲뻍쫇춶튪쪵쿖헻룶짺쏼훜웚훐뗄춶킧폃ퟮ듳[16]뮯ꆣ1992쓪ꎬLevy뫍Samuelsen 쳡돶쇋늻춬돖폐웚쿞쟩뿶쿂뗄놾닺뚨볛[17]컊쳢ꆣ춬쓪ꎬMarshall뫍Bansal 튲퓚웤ꆶ뷰죚릤돌ꆷ튻쫩훐뛔뛠웚쟩뿶쿂뗄CAPM쒣탍뷸탐쇋퇐뺿ꎬ퓚볙뚨떥뷗뛎쿠뛔쫕틦싊럾듓뛔쫽헽첬럖늼늢쟒춶ퟩ뫏뿉틔내웚뗷헻뗄쟩뿶쿂ꎬ횤쏷쇋CAPM튲쫇돉솢뿉틔쪹폃뗄ꆣ평폚뚯첬뻹횵-랽닮컊쳢쟳뷢뗄훖훖삧쓑ꎬ횱떽뷼쓪살뛠웚퇐뺿닅좡뗃뷏듳뷸햹ꆣ 2000쓪ꎬZhou [18] 뫍헫뛔춶훐듦퓚뛠웚뫍솬탸쪱볤뗄쟩탎붨솢쇋뻹횵-랽닮쒣탍ꎬ늢쟒퓚싛컄훐췆떼쇋쿔쪽뗄폐킧잰퇘뫍ퟮ폅뷢ꎬ붨솢쇋뚯첬춶ퟩ뫏톡퓱뗄뻹횵-퓚쿕놾쒣탍ꆣ 3ꆢ쳗샻뚨볛샭싛ꎨAPTꎩ 6
뗚튻헂 탷 싛 [5]1976쓪ꎬ쳡돶쇋쳗샻뚨볛샭싛ꎨArbitrage Pricing Theoryꎬ볲돆APTꎩꎬ퓚쯻뗄ꆶ놾닺뚨볛ꆪꆪ쳗샻뚨볛샭싛ꆷ튻컄훐횸돶ꎬ죎뫎닺뗄볛룱뿉틔뇭쪾캪튻킩ꆰ릲춬틲쯘ꆱ뗄쿟탔ퟩ뫏ꎬ벴놾쫐뎡훐쒳훖닺뗄볛룱뿉틔샻폃놾쫐뎡틔췢뗄웤쯻틲쯘쯹좷뚨ꆣ쳗샻뚨볛샭싛쫇퓚볙짨닺뗄풤웚쫕틦싊믡쫜튻킩캴횪믲헟쮵늻뿉풤닢틲쯘펰쿬뗄잰쳡쿂붨솢뗄ꎬ쳗샻뚨볛샭싛죏캪튻룶돤럖럖즢춶뗄닺ퟩ뫏ꎬ뷶탨튪벸룶쿠춬뗄틲쯘뻍뿉틔뷢쫍럧쿕늹뎥뗄펰쿬돌뛈ꎬ쟒떱쫐뎡듯떽튻훖뻹뫢ힴ첬쪱ꎬ닺뗄뻹뫢볛룱튲믡쪵쿖ꎬ쟒쫐뎡짏듋쪱늻믡듦퓚컞럧쿕쳗샻믺믡ꆣ 쿠뛔폚M-V쒣탍틔벰뫳살돶쿖뗄CAPM쒣탍ꎬAPT쫇붨솢퓚횤좯ퟩ뫏춶돤럖럖즢뗄볙짨잰쳡뗄믹뒡짏뗄ꎬ뿉틔쮵쫇튻훖럇뎣웓쯘뗄춶쮼쿫ꎬ벴ꆰ컞놾췲샻뗄쫂듳볒뚼믡닎폫ꆱꆣ떫쫇퓚쿖쪵쫐뎡ꎬ룷훖뢴퓓뗄쟩뿶붻횯펰쿬ꎬ쪹뗃컞럧쿕컞돉놾뗄쳗샻믺믡늻뿉쓜듦퓚ꆣ떫쫇ꎬ퓚뺺헹탔쫐뎡훐ꎬ평폚붻틗뗄룟킧탔ꎬ믡톸쯙쿻돽쳗샻믺믡ꆣ평폚룟킧ꎬ돉놾뫍럧쿕튲뻍믡틲듋뇤뗃뫜뗍ꆣ헢뻍폫APT샭싛뗄쮼쿫뷏캪뷓뷼ꆣ 4ꆢ폐킧쫐뎡샭싛 횤좯볛룱뿉틔돤럖랴펳쫐뎡짏폫막욱폐맘뗄좫늿탅쾢ꆣ늢쟒떱춶헟틔듋살좷뚨싲죫싲돶헾닟쪱ꎬ쎻폐죋뿉틔듓훐믱샻,헢뻍쫇폐킧쫐뎡샭싛ꎨEfficient [19][20]Market TheoryꎬEMTꎩꆣ1970쓪,Fama랢뇭쇋싛컄ꆶ폐킧놾쫐뎡ꎺ샭싛믘맋뫍뺭퇩ퟜ뷡ꆷꎬ뛔맽좥뗄폐킧쫐뎡볙쮵ꎨEfficient Markets Hypothesis,EMHꎩ[19]퇐뺿ퟶ쇋쾵춳짮죫뗄ퟜ뷡ꎬ늢쟒쳡돶쇋췪헻뗄샭싛퇐뺿뿲볜ꆣ 쿖퓚ꎬ폐킧쫐뎡샭싛쫇쿖듺쫐뎡샭싛뗄훘튪ퟩ돉늿럖ꎬ튲쫇횤좯춶ퟩ뫏샭싛퇐뺿뗄훘튪늿럖ꆣ놾쫀볍90쓪듺ꎬ톧헟쏇랢쿖쫐뎡듦퓚벾뷚탔ꆢ맽뛉랴펦뗈쿖쿳듦퓚ꆣ톧헟춳돆캪ꆰ틬쿳ꆱꎬ튻뛈톧헟쏇죏캪ꆰ틬쿳ꆱ쫇폫뛔쿖듺횤좯춶샭싛쿠뗄ꆣ떫쫇뫳살쯦ퟅ샭싛퇐뺿뗄짮죫ꎬ톧헟쏇훰붥랢쿖헢늢늻쓜럱뚨EMHꆣ[21]1999쓪ꎬBerk뗈횸돶ꎬ퓚ퟮ폅뚯첬춶맽돌훐ꎬ웳튵쯹쏦쇙뗄풤웚쫕틦싊뫍쾵춳럧쿕뚼쫇믡쯦ퟅ쪱볤뇤뮯뗄ꆣ싛컄뮹횸돶헋쏦쫐뎡뇈싊ꎨbook-to-market ratioꎩ폫풤웚쫕틦싊횮볤듦퓚뿉풤닢맘쾵ꆣ뮹폐튻킩쿠맘틲쯘ꎬ뇈죧뛌웚쓚뗄랴킧펦ꎨContrarian Effectsꎩ,샻싊뫍쫐뎡럧쿕틧볛횮볤뗄랴쿲맘쾵뚼쫇헽뎣쿖쿳ꆣ ꎨ죽ꎩ맺쓚퇐뺿쿖ힴ 7
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 뷼쓪살ꎬ쯦ퟅ맺쓚횤좯춶쫐뎡뗄량쯙랢햹ꎬ횤좯뗄춶ퟩ뫏샭싛뫍쒣탍퇐뺿틑뺭돉쇋떱잰톧쫵죈뗣ꆣ컒맺틔쳆킡컒ꆢ십폀뾪ꆢ퓸폂ꆢ믆뗇쫋캪듺뇭뗄튻엺톧헟ꎬ뷼킩쓪퓚헢킩랽쏦웄폐붨쫷ꆣ 퓚Alexander퓚1993쓪쫗듎쳡돶쇋쿞훆탔싴뿕뗄쒣탍뗄믹뒡짏ꎬ1997쓪퓸 [22]폂폫쳆킡컒뷸튻늽퇐뺿쇋퓊탭쿞훆탔싴뿕뗄쟩뿶쿂ꎬ횤좯ퟩ뫏춶폐킧뇟뷧뗄튻냣탔쳘헷ꎬ늢쟒룸돶쇋폐킧뇟뷧솬탸탔좷뚨랽램ꎬ듳듳뗄쳡룟쇋볆쯣킧싊ꆣ 웤뫳ꎬ헫뛔횤좯쫐뎡듦퓚싲뿕뫍싴뿕쿞훆벰뷨듻쿞훆뗈쿖쪵탔컊쳢ꎬ1999 [23]쓪ꎬ십폀뾪뫍쳆킡컒춨맽퇐뺿쇋싴뿕퓚횤좯춶ퟩ뫏훐뗄ퟷ폃ꎬ뗃돶퓚횤좯춶ퟩ뫏훐틑늻뻟폐춶믺탔뗄뷡싛ꎬ늢쟒쳡돶쇋솽훖탂뗄춶ퟩ뫏쒣탍ꎬ헢솽훖탂뗄춶ퟩ뫏뻶닟쒣탍샭싛짏쫊폃폚룼튻냣뗄쿞훆싴뿕춶뮷뺳쿂ꆣ [24]쇭췢ꎬ헫뛔늻퓊탭싴뿕뗄쟩뿶쿂뗄횤좯ퟩ뫏춶ꎬ십폀뾪뫍쳆킡컒쳡돶늻퓊탭싴뿕쟩뿶쿂뗄횤좯ퟩ뫏춶쒣탍ꎬ돆횮캪뛠톡짙쒣탍ꎬ늢룸돶쇋쫷탎쯣램틔뷢뻶쟳뷢컊쳢ꆣ [25]2001쓪ꎬ퓸폂ꆢ쳆킡컒뫍횣캬쏴퓚싛컄ꆶ믹뷰럖샫뚨샭뗄뷸튻늽퇐뺿ꆷ훐쳖싛쇋틽죫횸쫽웚믵뗄ퟩ뫏횤좯톡퓱폫믹뷰럖샫뚨샭ꎬ믹뷰럖샫뚨싉풴폚Markowitz퓚뻹횵-랽닮횤좯ퟩ뫏톡퓱쿂뗄솽믹뷰럖샫뚨싉ꎬ뷸튻늽쮵쏷쇋늻퓊탭싴뿕떫틽죫횸쫽웚믵뗄쟩뿶쿂폫퓊탭싴뿕쟩뿶쿂짺돉뗄뿉탐벯뗄ퟮ짙믹뷰횮볤뗄맘쾵ꆣ [26]2004쓪ꎬ역량ꆢ볖붨쏱뫍믆뗇쫋붫럧쿕-볛횵(risk-value)샭싛틽죫쇋춶ퟩ뫏톡퓱ꎬ틽죫쇋벫듳벫킡럧쿕볛횵ꎬ늢쟒붨솢쇋폫횮쿠뛔펦뗄ퟩ뫏춶쿟탔맦뮮쒣탍ꎬ퓚훐맺맺쓚춶ퟩ뫏샭싛퇐뺿훐ꎬ햼폐훘튪뗄뗘캻ꆣ 웤뫳ꎬ폐뫜뛠톧헟뫳살뚼쳖싛쇋VaR퓚춶ퟩ뫏훐뗄펦폃컊쳢ꆣ떫쫇ꎬ평폚VaR늻쓜듯떽춶ퟩ뫏럖즢뮯뗄좱쿝ꎬCVaRꎨ쳵볾럧쿕횵ꎩ놻톧헟쳡돶ퟷ캪뛔VaR뗄튻훖탞헽ꆣ [27]2004쓪ꎬ샮톡뻙뫍룟좫쪤퓚웤싛컄ꆶ붻틗럑폃뫍CVaR럧쿕닢뛈쿂뗄컈붡춶ퟩ뫏ꆷ훐쳖싛쇋퓚뾼싇붻틗럑폃뗄잰쳡뫍CVaR럧쿕닢뛈쟩뿶쿂횤좯춶ퟩ뫏뗄컈붡탔컊쳢ꎬ늢쟒퓚싛컄훐샻폃튻냣쿟탔맦뮮랽램뛔웤쒣탍뗄폐킧탔뷸탐쇋퇩횤ꆣ [28]2005쓪ꎬ역듳뫢뫍튦풪뛋퓚싛컄ꆶ듸믺믡풼쫸뗄뚯첬춶뻶닟쒣탍퇐뺿ꆷ8
뗚튻헂 탷 싛 훐퇐뺿쳖싛쇋틽죫CVaR뗄ퟮ폅뚯첬춶뻶닟쒣탍ꎬ컄헂뻟쳥뗘퇐뺿쇋퓚뚯첬쟩뿶쿂뻟폐믺믡풼쫸뗄춶닟싔늢쟒붨솢쇋뻶닟쒣탍ꆣ랢햹떽뷱쳬ꎬ틔CVaRퟷ캪럧쿕뛈솿뷸탐춶ퟩ뫏톡퓱뗄퇐뺿뿉틔쮵틑뺭쫇떱뷱톧쫵뷧뗄퇐뺿죈뗣ꆣ 훬쫩짐폚2003쓪퓚ꆶ뛠뷗뛎춶ퟩ뫏톡퓱벰웤럧쿕뿘훆ꆷ튻컄훐횸돶ꎺ솬[29]탸쪱볤ힴ첬쪵볊짏쫇샫즢쪱볤ힴ첬뗄췆맣탎쪽ꆣ듓쿖쪵뗄뷇뛈ꎬ틲캪솬탸쪱볤쒣탍붨솢뗄듦퓚뗄삧쓑뫍늻뿉닙ퟷ탔ꎬ뛠뷗뛎뗄ퟩ뫏춶ퟩ뫏쒣탍뿉틔퓚샫즢쪱볤쒣탍뗄믹뒡짏췆맣ꆣ떫쫇ꎬ샫즢쪱볤M-V쒣탍뗄퇐뺿돉맻놾짭튲쫇늢늻럡뢻뗄ꎬ쯹틔뛠웚춶ퟩ뫏쒣탍튻횱쫇퇐뺿뗄죈뗣컊쳢ꆣ [6]2004쓪ꎬ슷펦뷰ꎬ쳆킡컒ꎬ훜ퟚ럅퓚쟸볤쫽틑뺭듳솿펦폃폚쒣뫽뻶닟뗄믹뒡짏ꎬ쳡돶쇋틽죫쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍뗄쿟탔맦뮮랽램ꎬ퓚싛컄훐ꎬ춨맽틽죫뫢솿춶헟뗄럧쿕쾲뫃돌뛈뗄럧쿕욫뫃쾵쫽α듓뛸붫쟸볤쫽뗄쿟탔맦뮮뮯캪쿟탔맦뮮ꎬ늢춨맽쪵횤룸폨횤쏷ꆣ웤뫳ꎬퟷ캪퇐뺿뗄죈뗣컊쳢ꎬ뫜뛔톧헟뛔믹폚쟸볤쫽뗄쒣뫽쟩뿶쿂뗄횤좯ퟩ뫏춶쒣탍뷸탐쇋퇐뺿ꆣ2007쓪ꎬ돂뮪폑,[30]헔폱쎷퓚ꆶ믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍퇐뺿ꆷ튻컄훐ꎬ뛔웤뷸탐쇋뷸튻늽뗄퇐뺿쮵쏷ꎬ쯦ퟅ쒣뫽뻶닟뗄랢햹ꎬ룷훖늻좷뚨틲쯘놻풽살풽뛠뗄펦폃떽횤좯ퟩ뫏춶훐ꎬ샽죧쟸볤쫽뗄펦폃뗈ꆣ헢튲쪹횤좯ퟩ뫏춶뻶닟룼뻟폐죡탔ꎬ튲폫쿖쪵쟩뿶룼볓쳹뷼ꆣ 쯄ꆢ놾컄뷡릹ꆢ퇐뺿랽램폫뒴탂뗣 ꎨ튻ꎩ놾컄뷡릹 놾컄뗄뗚튻헂닻쫶쇋싛컄뗄퇐뺿놳뺰폫퇐뺿틢틥ꆣ뗚뛾헂헫뛔컄헂짦벰뗄훷튪샭싛뷸탐쇋ퟛ쫶ꎬ뛔폚샭싛뗄쿠맘룅쓮룸돶쇋짮죫잳돶뗄닻쫶ꆣ 뗚죽헂퓚Markowitz뻹횵-랽닮쒣탍뗄샭싛믹뒡짏쳖싛쇋틽죫쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍ꎬ룸돶튻훖쟸볤쒣뫽쫽횤좯춶ퟩ뫏쿟탔맦뮮쒣탍ꎬ늢붫쒣탍뮯캪튻냣닎쫽쿟탔맦뮮뷸탐쟳뷢ꆣ 뗚쯄헂닉폃횸쫽욽뮬풤닢헢훖뷏캪뿆톧뗄랽램살쟳좡풤웚쫕틦싊뗄쟸볤쒣뫽쫽ꎬퟮ뫳룸돶쒣탍쟳뷢뷡맻ꎬ횤쏷쇋쒣탍뗄폐킧탔ꆣ 뗚컥헂룸돶쇋싛컄뗄ퟜ뷡뫍늻ퟣꎬ늢뛔캴살뗄퇐뺿잰뺰ퟷ쇋햹췻ꆣ 9
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 룹뻝훐맺횤좯쫐뎡뗄랢햹쿖ힴ틔벰횤좯춶샭싛ꆢ 퇐뺿릹쮼 쒣뫽뻶닟샭싛뗄랢햹쿖ힴ좷뚨퇐뺿쒿뗄틔벰퇐뺿 틢틥 춨맽컄쿗ퟛ쫶ꎬퟜ뷡틔췹맘폚횤좯춶ퟩ뫏쒣탍뻶 샭싛ퟛ쫶 닟뗄퇐뺿돉맻 톡좡20횧짏쫐릫쮾막욱뗄2009쓪3퓂6죕떽2010쓪3 쫽뻝쫕벯 퓂5죕뗄20훖막욱뗄뾪엌볛뫍쫕엌볛ꎬ볆쯣뷸탐쫕 틦뫍럧쿕쯰쪧싊랶캧좷뚨 뛔쫽뻝뒦샭뷡맻붨솢쿟탔맦뮮쒣탍ꎬ뷸탐쪵횤럖 쪵횤럖컶 컶,늢뛔쯹뗃뷡맻뷸탐쳖싛쮵쏷 ퟜ뷡퇐뺿돉맻,쏷좷퇐뺿틢틥,쳡돶캴살퇐뺿뗄룄 퇐뺿ퟜ뷡 뷸랽쿲 1-1 컄헂뿲볜 ꎨ뛾ꎩ퇐뺿랽램 1ꆢ컄쿗퇐뺿램ꎺ춨맽뛔횤좯춶ퟩ뫏샭싛ꆢ쒣탍뫍쯣램벰쿖듺뻶닟샭싛뫍랽램뗄퇐뺿ꎬ헒돶쿖듺춶뻶닟쒣탍뗄훷튪뒴탂랽쿲ꎬ늢뷡뫏죡탔뻶닟헢룶떱잰퇐뺿죈뗣ꎬ틽죫쟸볤쫽ꎬ캪쪹춶뻶닟룼죡탔쳡릩믹뒡ꆣ 2ꆢ쪵횤퇐뺿램ꎺ톡좡쿖쪵짏쫐릫쮾막욱볆쯣돶훜쫕틦싊ퟷ캪짨뚨풤웚쫕틦싊랶캧뗄틀뻝ꎬ틽죫횸쫽욽뮬램룹뻝췹웚쫽뻝볆쯣뗃돶쟸볤쫽쒣뫽춶ퟩ뫏쒣탍뗄쫕틦쟸볤뫍럧쿕쟸볤ꆣ붨솢쿟탔맦뮮쒣탍ꎬ룹뻝쿖쪵훐춶헟뗄탄샭캪틀뻝ꎬ짨뚨룼뫏샭뗄럧쿕욫뫃닎쫽뫍쒿뇪몯쫽폅뮯쮮욽닎쫽, 닉폃lingo죭볾뛔늻춬뗄닎쫽횵뷸탐퇐뺿ꎬ뗃돶뻶닟뷡싛ꆣ ꎨ죽ꎩ싛컄뒴탂뗣 1ꆢ뇈뷏쇋벸훖틽죫쟸볤쒣뫽쫽뗄죡탔횤좯춶ퟩ뫏뻶닟쒣탍ꎬ붨솢쇋튻훖볆쯣뷏캪볲뇣뗄쟸볤쒣뫽쫽춶ퟩ뫏쒣탍뷸탐횤좯ퟩ뫏춶뻶닟뗄쪵폃탔럖컶ꆣ 2ꆢ뛠쫽톧헟퇐뺿쟸볤쒣뫽쫽뗄횤좯춶ퟩ뫏쒣탍뚼뷶뷶쫇횤쏷쒣탍뗄뿉탐10
뗚튻헂 탷 싛 탔ꎬ쎻폐ퟅ훘럖컶웤퓚쿖쪵춶훐닎뾼볛횵ꎬ쪵횤쪱톡좡막욱뷏짙ꎬ뛸쟒풤닢쫕틦싊뗄볆쯣좱짙샭싛틀뻝ꎬ폐뗄췑샫쪵볊쟩뿶ꎬ평듋퓬돉뗄쒣뫽쟸볤늻쓜뫜뫃뗄랴펦쪵볊쟩뿶ꎬ헢퇹춻돶쇋죡탔뻶닟뗄쳘뗣떫쫇폐쪱폖쿔뗃맽폚ꆰ죡탔ꆱꆣ헢죃쒣탍퓚쪵볊펦폃훐뗄뫜뛠컊쳢뚼쎻폐놻뫜뫃뗄뷢뻶ꎬ튲죃쒣탍뗄쪵폃탔듳듳헛뿛ꆣ놾컄룹뻝짏몣횤좯붻틗뗄20훖막욱럖컶룃쒣탍뗄쪵볊펦폃볛횵ꎬ늢쟒룹뻝샭싛컄쿗닉폃룸돶쇋튻훖뷏캪뫏샭뗄풤웚쫕틦쟸볤뫍럧쿕쯰쪧싊쟸볤뗄볆쯣뫍좷뚨랽램ꆣ 3ꆢ뛔폚쟸볤쫽횤좯춶ퟩ뫏쒣탍퓚훐맺횤좯쫐뎡ퟩ뫏춶뫍믹뷰톡막짏뗄펦폃룸돶쇋뷡싛뫍붨틩ꆣ 11
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 뗚뛾헂 쿠맘샭싛ퟛ쫶 퓚쿖쪵뮷뺳훐ꎬ횤좯쫐뎡뗄펰쿬틲쯘뗄늻좷뚨탔ꎬ쪹뗃춶헟퓚ퟶ춶뻶닟쪱튲믡쏦쇙룷훖뗄늻좷뚨ꆣ쯦ퟅ뷼킩쓪살횤좯쫐뎡뗄랢햹뫍쒣뫽샭싛뗄랢햹ꎬ듸뚯ퟅ횤좯쫐뎡뗄쒣뫽탔뻶닟샭싛튲량쯙랢햹웰살ꎬ뫜뛠톧헟죏캪평폚횤좯쫐뎡뗄쯦믺탔뫍쒣뫽탔ꎬ뻶뚨쇋횤좯쫕틦싊뗄늻좷뚨탔ꆣ뛸뛔폚탨튪ퟷ돶뻶닟뗄횤좯춶죋풱믲헟쮵춶헟살쮵ꎬ웤쓚탄웚췻뗄쫕틦싊튲늢늻쫇튻룶좷뚨쫽횵ꆣ쟸볤쫽ퟷ캪쒣뫽쫽뗄튻샠ꎬ튻횱쫇뒦샭룃샠늻좷뚨탔뻶닟뗄폐솦릤뻟ꆣ쟸볤쫽뗄춶ퟩ뫏컊쳢쫇뻟폐뷏잿퇐뺿틢틥늢쟒뻟폐뫜잿뗄쿖쪵틢틥뗄ꆣ 튻ꆢ믹폚쒣뫽틢틥쿂뗄춶ퟩ뫏쒣탍 [31]1965쓪ꎬZadeh쳡돶쇋쒣뫽벯뫏뗄룅쓮ꎬ뒴솢쇋쒣뫽벯뫏싛ꎬ늢쟒룸돶쇋쿖쪵짺믮훐쓑틔폃룅싊뇭쪾뗄쒣뫽쿖쿳뷸탐뚨솿쏨쫶ꆢ럖컶뫍퓋쯣뗄랽램ꆣ1975[32]쓪ꎬBellman뫍Zadeh퓚뛠쒿뇪뻶닟뗄믹뒡짏붨솢쇋쒣뫽뻶닟뗄쒣탍,늢쟒룸돶쇋랲쫇뻶닟훐늻쓜뺫좷좷뚨뗄닎쫽ꎬ뚼뿉틔틔쒣뫽벯뫏뗄탎쪽룸돶ꆣ [33]Kwakernaak폚1978쓪쳡돶쇋튻룶뿉틔춬쪱랴펳쒣뫽탔뫍쯦믺탔뗄늻좷뚨탔뇤솿-쒣뫽쯦믺뇤솿뗄뚨틥ꎬ뾪뒴쇋솽훖틲쯘춬쪱퇐뺿뗄쿈뫓ꎬ뻟폐훘튪틢틥ꆣ웤뫳ꎬ뫜뛠톧헟뾪쪼샻폃헢훖쒣뫽쯦믺뇤솿뗄룅쓮ꎬ뾪쪼뷸탐쒣뫽뮷뺳쿂뗄춶ퟩ뫏뗄퇐뺿뫍쒣뫽뮷뺳쿂뗄뻶닟컊쳢퇐뺿ꆣ [34]1998쓪ꎬRamaswamy쳡돶쇋튻훖믹폚쒣뫽뻶닟샭싛뗄춶ퟩ뫏톡퓱쒣탍ꆣ헢훖쒣뫽뻶닟춶ퟩ뫏쒣탍쫇퓚춨맽볙짨춶ퟩ뫏퓚쿖쪵쫐뎡뗄쫕틦캪쒣뫽뇤솿뗄듳잰쳡쿂ꎬ퓚뛠쒿뇪뻶닟랽램뗄믹뒡짏릹붨춶헟뛔춶ퟩ뫏쫕틦싺틢돌뛈뗄솥쫴몯쫽ꎬ좻뫳붨솢싺틢뛈듯떽ퟮ듳뗄춶ퟩ뫏톡퓱쒣탍ꆣ볙짨춶헟쫇퓚믹폚쒳룶쫐뎡쟩뺰쿂살릹퓬춶ퟩ뫏ꎬ뛔닺i(i=1,2",n)짨뚨돶ퟮ킡뫍ퟮ듳뗄춶뇈샽ꎬ뛸뛔쎿훖쫐뎡쟩뺰ꎬ춶헟뚼뻟폐튻룶쒿뇪랶캧ꎬ룸뚨ퟮ듳뫍ퟮ킡웚췻쫕틦ꎬ붨솢춶헟뛔춶쫕틦싺틢돌뛈뗄솥쫴몯쫽ꎬ짨뚨킡폚ퟮ킡횵쪱ꎬ솥쫴뛈α=0ꎬ듳폚ퟮ듳횵뗄ꎬ솥쫴뛈α=1ꎬ뷩폚횮볤뗄ꎬ룸뚨튻룶솥쫴몯쫽ꎬ듓뛸듓춶헟쫕틦ퟮ듳뮯뗄뷇뛈뷸탐춶뻶닟ꆣ떫쫇Ramaswamy뗄쒣탍쎻폐뾼싇떽럧쿕12
뗚뛾헂 쿠맘샭싛ퟛ쫶 폫쫕틦횮볤뗄쿠뮥맘쾵ꎬ쇷뚯탔믲헟쮵뮻쫖싊뗈튻쾵쇐컊쳢ꎬ뷶뷶듓쫕틦ퟮ듳뮯뗄뷇뛈살뷸탐뻶닟ꎬ뛸쟒평폚룸돶솥쫴몯쫽뗄삧쓑탔ꎬ뮹폐뫜듳뗄췪짆뫍퇐뺿뗄뿕볤ꆣ뷼킩쓪살ꎬ쯦ퟅ뛠쫴탔뻶닟샭싛뫍랽램뗄랢햹ꎬ죃쒣뫽뮷뺳쿂뗄춶ퟩ뫏뾼싇떽룼뛠뗄펰쿬틲쯘뾪쪼놻톧쫵뷧쯹훘쫓ꆣ 뛾ꆢ쿖듺뛠ힼ퓲뻶닟샭싛 튻냣살쮵ꎬ톧쫵뷧붫뛠ힼ퓲뻶닟럖캪뛠쫴탔뻶닟ꎨMADMꎩ뫍뛠쒿뇪뻶닟(MODM)솽훖ꆣ ꎨ튻ꎩ뛠쫴탔뻶닟뗄샭싛뫍랽램 뛠쫴탔뻶닟쫇룹뻝뻶닟컊쳢뗄뛠룶쫴탔ꎬ틀뻝쪹뗃뻶닟헟뗄웚췻뗄싺틢돌뛈[35]쓜듯떽ퟮ듳뮯뗄풭퓲살톡퓱ퟮ병랽낸ꆣ [36]ꆢ뫍퓚1957쓪퓚싛컄훐샻폃쫽톧훐뗄볲떥볓좨램살뒦샭짌튵춶훐뗄뻟쳥뗄뻶닟컊쳢ꆣ톧쫵뷧튻냣죏캪헢쫇뛠쫴탔[37]뻶닟뗄ퟮ퓧퇐뺿ꆣ폚1973쓪랢뇭뗄싛컄훐쫕벯쇋쫽쪮훖뛠쫴탔뻶닟뗄쪵폃뒦샭랽램ꎬ뷸탐쇋럖샠늢쟒룸돶쇋ퟔ벺뒴탂뗄퇐뺿랽램ꆣ [38]20쫀볍80쓪듺ꎬ뫍뫏ퟷ돶냦쇋맘폚뛠쫴탔샭싛ꆢ랽램뫍펦폃뗄훸ꎬ쾵춳뗄ퟜ뷡쇋틔췹뗄퇐뺿돉맻ꎬ룸돶쇋뛠쫴탔뻶닟뗄뚨틥ꎬ늢쟒뛔뛠쫴탔뻶닟뗄랽램뷸탐쇋쾵춳럖샠ꆣ퓚훸ퟷ훐ꎬ뛠쫴탔뻶닟컊쳢놻내헕뻶닟헟욫뫃탅쾢뗄늻춬럖캪죽샠ꆣ1ꆢ컞욫뫃탅쾢뗄뛠쫴탔뻶닟ꎬ헢샠컊쳢튻냣닉좡맅뗤뻶닟랽램살뷢뻶ꎬ뇈죧벫듳벫킡풭퓲ꎬ벫듳벫듳풭퓲뗈ꆣ2ꆢ룸돶쫴탔욫뫃탅쾢뗄뛠쫴탔뻶닟ꎬ헢훖뻶닟쿠뛔살쮵뷏캪뢴퓓ꎬ뿉룹뻝쫴탔뗄뻟쳥쟩뿶닉폃쳞돽램ꆢퟖ뗤탲램ꆢ업쇐램ꆢ쿟탔럖엤램ꆢ닣듎럖컶램뗈랽램뻟쳥럖컶ꆣ3ꆢ룸돶랽낸욫뫃탅쾢뗄뛠쫴탔뻶닟ꆣ헢샠컊쳢뷏캪뢴퓓ꎬ튲쫇뷼쓪살뗄퇐뺿죈뗣ꆣ 퓚쿖쪵짺믮훐ꎬ뻶닟헟뎣뎣믡폶떽뻶닟탅쾢늻쏷좷뗄쟩뿶ꎬ헢튲뻍쫇톧쫵짏쯹쮵뗄늻좷뚨탔믲헟쒣뫽탔ꆣ뷼킩쓪살ꎬ믹폚쟸볤쫽뗄뛠쫴탔컊쳢뗄퇐뺿틑뺭쫇뷢뻶듋샠뻶닟컊쳢뗄튻룶훘튪랽램뫍샭싛퇐뺿뗄튻룶훘튪ퟩ돉늿럖ꆣ ꎨ뛾ꎩ뛠쒿뇪뻶닟뗄샭싛뫍랽램 뷸탐뻶닟쪱ꎬ뻶닟헟튪내쒳훖뇪ힼ듓뿉릩톡퓱뗄랽낸훐톡돶ퟮ싺틢뗄랽낸ꆣ죴쫇쯹ퟷ뗄뻶닟횻폐튻룶톡퓱뇪ힼꎬ헢뻍쫇떥쒿뇪뻶닟ꆣ떫쫇쿖쪵훐룼뛠뗄튻룶13
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 뻶닟튪듯떽뛠룶쒿뇪뗄ퟮ폅뗄뻶닟컊쳢ꎬ샽죧퓚횤좯춶ퟩ뫏톡퓱훐뻍볈튪뾼싇풤웚쫕틦뺡뿉쓜뗄듳춬쪱돐쫜뗄럧쿕폖튪뺡뿉쓜킡ꆣ헢킩쒿뇪췹췹쫇쿠뮥훆풼ꎬ쿠뮥쎬뛜뗄ꆣ뇈죧횤좯쫕틦룟뫍뗍럧쿕뮥쿠쎬뛜뗄ꆣ뛠쒿뇪맦뮮뻍쫇퇐뺿헢샠뛠쒿뇪ퟮ폅컊쳢뗄튻훖쫽톧랽램ꆣ튻냣죏캪ꎬ뛠쒿뇪뻶닟쫇퓚뾼싇퓚폐쿞풴뗄쿞훆뫍뻶닟컊쳢훐뗄랽낸쎻폐뻟쳥룸뚨뗄쳵볾쿂ꎬ헒떽튻룶싺ퟣ쯹폐쒿뇪쪹웤뻶닟[39]뷡맻ퟮ폅뗄ퟮ병랽낸ꆣ [39]1953쓪ꎬArrow뗈죋퓚잰죋퇐뺿뗄믹뒡짏쳡돶쇋폐킧뗣뗄룅쓮뫳ꎬ뛠쒿뇪뻶닟훰붥돉캪톧쫵죈뗣ꆣ뛠쒿뇪뻶닟컊쳢ퟮ쿔훸뗄쳘뗣뻍쫇쒿뇪볤뗄늻뿉릫뛈탔뫍쒿뇪볤듦퓚쎬뛜탔ꆣ쒿뇪훐뗄늻뿉릫뛈탔뻍쫇횸룷룶쒿뇪횮볤쎻폐튻룶뿉춳튻뗄뛈솿뇪ힼꎬ뛸쎬뛜탔쫇횸떱닉폃쒳튻룶랽낸좥룄뷸쒳튻쒿뇪횵쪱ꎬ믡돶쿖쪹쇭튻쒿뇪횵뇤뫃믲헟뇤뮯뗄쟩뿶ꆣ평폚헢룶쳘헷ꎬ쯹틔뛠쒿뇪뻶닟뻍늻쿱떥쒿뇪뻶닟쓇쎴볲떥ꆣ [39]쎿룶뛠쒿뇪뻶닟짦벰5룶믹놾튪쯘ꎺ T1ꆢ뻶닟뇤솿x=(x,x,",x) 12nT2ꆢ쒿뇪몯쫽f(x)=(f(x),f(x),",f(x)), m≥2 12mnn3ꆢ뿉탐뷢벯X⊆\,X=x∈\g(x)≤0,i=1,2,",p,h(x)=0,r=1,2,",q {}ir4ꆢ욫뫃맘쾵 퓚쿱벯f(X)=f(x)x∈X훐듦퓚쒳뛾풪맘쾵≺랴펳뻶닟헟뗄욫뫃ꆣ {} 5ꆢ뷢뗄뚨틥ꆣ퓚틑횪욫뫃맘쾵≺쿂컒쏇뚨틥쫇퓚X짏뗄ퟮ폅뷢ꆣ f [39]뛠쒿뇪뻶닟뗄컊쳢튻냣뿉폃죧쿂릫쪽쏨쫶캪ꎺ minf(x)=(f(x),f(x),",f(x))12mg(x)≤0,i=1,2,",p (2-1) ,h(x)=0,r=1,2,",qr웤훐x캪n캬뻶닟쿲솿ꆣ웤뿉탐폲캪 nX=x∈\g(x)≤0,i=1,2,",p,h(x)=0,r=1,2,",q {}ir퓚뛠쒿뇪맦뮮컊쳢훐ꎬ튻냣쟩뿶쿂늢쎻폐튻룶뷢쓜쪹쯹폐쒿뇪몯쫽춬쪱듯떽ퟮ폅뮯ꆣ쯹틔퓚뛠쒿뇪뻶닟훐뻸뛔ퟮ폅뷢쫇늻듦퓚뗄ꎬ뛸쫇쇭튻훖뷢뗄룅쓮ꎺ폐킧뷢ꆣ짨뿉탐뷢x쫇폐킧뷢ꎬ웤몭틥쫇늻듦퓚뇰뗄뿉탐뷢′x쓜쪹웤쒿뇪몯쫽횵14
뗚뛾헂 쿠맘샭싛ퟛ쫶 ′f(x)킡폚믲뗈폚뿉탐뷢x뗄룷룶쒿뇪몯쫽횵f(x)(k=1,2,",m)늢쟒듦퓚훁짙kk[39]튻룶kꎬ′f(x)퇏룱킡폚f(x)ꆣ 0kk00퓚뛠쒿뇪뻶닟훐ꎬ폐킧뷢벯훐뗄폐킧뷢믡럇뎣뛠ꎬ뻶닟헟룹뻝ퟔ벺뗄훷맜에뛏살톡좡랽낸ꎬ죧맻쯻죏캪랽낸x뇈′x뫃ꎬ퓲뚨틥퓚X짏뗄뛾풪맘쾵ꎬ돆캪욫뫃탲ꆣ뻶닟헟룹뻝뻶닟풭퓲퓚폐킧뷢벯훐뷸탐좨뫢톡퓱돶싺틢뷢ꆣ컒쏇폃튻룶킧폃몯쫽u(f(x),f(x),",f(x))살뇭쪾뻶닟헟뗄욫뫃ꎬ퓲쪹u듯떽ퟮ듳횵뗄폐킧뷢뻍12m[39]쫇뻶닟헟뗄싺틢뷢ꆣ뛠쒿뇪쿟탔맦뮮컊쳢뻍뇤돉쇋ꎺ maxu(f(x),f(x),",f(x))12m (2-2) ∈X쿖퓚톧쫵뷧튻냣폃움볛몯쫽램ꆢ쒿뗄맦뮮램ꆢ럖닣탲쇐램ꆢ붻뮻맦뮮램뫍솥쫴몯쫽램살뷢뻶컊쳢ꆣ 쒿잰ꎬ뛠쒿뇪뻶닟퓚샭싛뫍펦폃훐뚼좡뗃튻킩훘튪돉맻ꎬ웤펦폃랶캧튲풽살풽맣랺ꎬퟷ캪튻룶릤뻟퓚릤돌ꆢ뺭볃ꆢ맜샭ꆢ뻼쫂뗈쇬폲뗄뻶닟컊쳢짏웰떽뻞듳뗄ퟷ폃ꆣ 죽ꆢ쟸볤쫽샭싛 쟸볤쫽쫇쒣뫽쫽뗄튻훖ꎬ쫇뒦샭늻좷뚨탔컊쳢뗄폐킧릤뻟ꆣ퓚죡탔뻶닟랢햹돉죈뗣뗄뷱쳬ꎬ쟸볤쫽풽살풽뛠뗄돶쿖퓚듋샠뻶닟컊쳢훐ꆣ 쟸볤쫽뗄뚨틥뫍퓋쯣램퓲ꎺ 40[]뚨틥1.짨쯹폐뗄쪵쫽벯뫏캪ℜꆣ짨a=a,a쫇폐뷧뗄뇕쟸볤ꎬ죴a≤a,쟒aa∈ℜ,퓲돆a=a,a캪쟸볤쫽ꆣ웤훐쫇쟸볤쫽뗄쿂뷧ꎬa쫇쟸볤쫽뗄짏뷧ꆣ [40]뚨틥2.뎣폃쟸볤쫽뗄퓋쯣맦퓲ꎺ −A=a,a,B=[b,b] −−⇒A+B=[a+b,a+b] −−−A−B=[a−b,a−b] −−15
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 kA=[ka,ka],k>0 −kA=[ka,ka],k≤0 −[40]뚨틥3.쟸볤쫽탲맘쾵ꎺ−A≤B⇐⇒a≤b,a≤b −−A<B⇐⇒A≤B쟒A≠B쯄ꆢ떥쿮풤닢랽램 떥쿮풤닢랽램쫇ퟩ뫏풤닢랽램뗄믹뒡ꎬ뎣폃뗄떥쿮풤닢랽램냼삨쪱볤풤닢쒣탍ꆢ믘맩풤닢쒣탍ꆢ쯦믺쪱볤탲쇐풤닢쒣탍ꆢ믒즫쾵춳풤닢쒣탍ꆢ벾뷚뇤뚯쪱볤탲쇐뗄풤닢쒣탍뗈ꆣ 쪱볤탲쇐쫇횸ퟔ좻쿖쿳믲헟짧믡뺭볃쿖쿳뗄쒳샠횸뇪내헕쪱볤뗄쿈뫳쮳탲[41]쯹업쇐돉뗄쫽ퟖ탲쇐ꆣ튻냣쪱볤탲쇐뗄뇭듯쪽쫇x,=1,2,",nꎬ샯쏦냼몬솽{}t룶튪쯘ꎺ튻룶쫇쿖쿳쯹퓚뗄쪱볤ꎬ튻룶쫇퓚듋쪱볤쿠뛔펦뗄횸뇪횵ꆣ쪱볤탲쇐풤닢쒣탍냼삨뗄뺭뗤쒣탍폐뻟폐뻖늿쮮욽쟷쫆뗄욽뮬풤닢쒣탍ꆢ뻟폐쿟탔쟷쫆뗄췢췆풤닢쒣탍ꆣ 뻟폐뻖늿쮮욽쟷쫆뗄욽뮬풤닢쒣탍훐뗄횸쫽욽뮬풤닢랽램뿉틔퓚틑횪쒳쪱볤뛎쪱볤탲쇐횸뇪뗄믹뒡짏ꎬ뛔쿂튻쪱뿌뗄쪱볤탲쇐횸뇪뷸탐풤닢ꆣ틲듋퓚춶[42,43]뗄뻶닟훐뎣폐펦폃ꆣ 횸쫽욽뮬풤닢램뗄볆쯣릫쪽쫇 n−11−ωiˆ x=λx+λx+"λx=x (2-3) n+10n1n−1n−11∑n−in1−ωi=0웤훐ˆx뇭쪾n+1쪱뿌쪱볤탲쇐횸뇪뗄풤닢횵ꆣ n+1n틲캪ω∈ꎨ0ꎬ1ꎩꎬ쯹틔limω=0ꎬ듓뛸 x→+∞∞iˆx=(1−ω)ωx (2-4) n+1∑n−i=0쇮α=1−ω,퓲α∈0,1ꎬω=1−αꎬ퓲 ()16
뗚뛾헂 쿠맘샭싛ퟛ쫶 ∞ix=α(1−α)x (2-5) n+1∑n−i=0웤훐α돆횮캪욽뮬쾵쫽ꆣ 1ꆢ훷맛램ꆣ훷맛램쫇룹뻝쪱볤탲쇐뗄횸뇪횵뗄뇤뮯쟩뿶살좷뚨욽뮬쾵쫽뗄튻훖랽램ꆣ퓚듋훖풤닢랽램훐ꎬα뗄톡좡폐훷맛램뫍뿍맛램솽훖ꆣ 떱쪱볤탲쇐뗄횸뇪횵뇤뮯럹뛈뷏킡쪱ꎬα뿉틔좡퓚ퟳ폒ꎬ떱쪱볤탲쇐뗄횸뇪횵뇤뮯럹뛈뷏듳쪱ꎬα튻냣좡횵퓚뫍횮볤뷏캪뫏쫊ꆣ 2ꆢ뿍맛램ꆣ뿍맛램쫇튻훖룹뻝횸쫽욽뮬풤닢랽램샻폃퓚쓢뫏쟸볤짏뗄컳닮욽랽뫍횸뇪ퟮ킡뮯듓뛸쟳돶ퟮ폅α뗄튻훖랽램ꆣ nn22Qeˆ==(x−x) (2-6) ∑∑tttt=1t=1웤훐Q뇭쪾횸쫽욽뮬풤닢램퓚쓢뫏쟸볤짏컳닮뗄욽랽뫍ꎻ e캪욽뮬쾵쫽α뗄몯쫽ꆣ퓲α뗄컊쳢뿉폃쿂쏦뗄ퟮ폅뮯쟳뷢뗃돶ꆣ tn2miˆnQ=(x−x) (2-7) ∑ttα∈(0,1)t=1쪱볤탲쇐풤닢쒣탍뿉틔틀뻝틔췹뗄쒳룶쪱볤뛎뗄쫽횵ꎬ풤닢돶횮뫳쒳뛎쪱볤뗄횸뇪횵ꆣ 짏쏦쳡떽쇋쪱볤탲쇐풤닢쒣탍뿉틔뛔캴살쪱볤뛎뗄횸뇪횵뷸탐풤닢ꆣ떫쫇헢훖풤닢뎣뎣믡닺짺튻훖훍뫳뗄쟩뿶ꆣ폶떽헢훖쟩뿶튻냣닉폃뻟폐쿟탔쟷쫆뗄췢췆풤닢쒣탍훐뗄뛾듎틆뚯욽뻹풤닢쒣탍믲헟뛾듎횸쫽욽뮬풤닢쒣탍뛔헢훖훍뫳탔뷸탐룄뷸ꆣ 펢맺뿆톧볒Galton퓚퇐뺿틅뒫컊쳢쪱틲캪튪뒦샭듳솿쫽뻝ꎬ랢쿖쇋믘맩쿖쿳ꆣ믘맩럖컶풤닢랽램쫇퇐뺿튻룶쯦믺뇤솿폫쇭췢튻룶쯦믺뇤솿믲헟벸룶뇤솿횮볤뗄쫽솿맘쾵ꎬ좻뫳폃헢훖맘쾵살풤닢쒳룶쯦믺뇤솿뗄튻훖쫽톧풤닢랽램ꆣ 믘맩럖컶풤닢랽램내헕쒣탍랽돌몬폐뗄뇤솿뗄쫽쒿뿉틔럖캪튻풪믘맩뫍뛠풪믘맩ꎬ내헕랽돌뗄탔훊뿉붫랽돌럖캪쿟탔믘맩뫍럇쿟탔믘맩ꆣ 1968쓪ꎬ훸쏻춳볆톧볒Jenkins뫍Box퓚쯦믺쪱볤탲쇐샭싛뗄믹뒡짏ꎬ돶냦[44]쇋ꆶ쪱볤탲쇐럖컶ꆪꆪ풤닢뫍뿘훆ꆷ튻쫩뛔쯦믺쪱볤탲쇐쒣탍뗄쪶뇰ꆢ닎쫽맀볆ꆢ헯뛏볬퇩뫍쿠맘붨쒣랽램뷸탐쇋쾵춳뗄닻쫶ꆣ뛔폚만뚨쪱볤tꎬy캪튻룶쯦t17
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 믺뇤솿ꎬ컒쏇냑y,t=1,2,"돆캪튻룶쯦믺뇤솿탲쇐ꎬ냑y,t∈−∞,+∞돆캪{}{()}tt튻룶쯦믺맽돌ꆣ 튻냣톧쫵짏뎣폃뗄쯦믺쪱볤탲쇐풤닢쒣탍폐욽컈쪱볤탲쇐ꆢ욽컈쯦믺쪱볤탲쇐쒣탍ꆢ욽컈쯦믺쪱볤탲쇐쒣탍뗈ꆣ쯦믺쪱볤탲쇐퓚웸뫲ꆢ쮮컄ꆢ뺭볃뗈랽쏦뗄풤닢훐폐맣랺펦폃ꆣ 18
뗚죽헂 쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍퇐뺿 뗚죽헂 쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍퇐뺿 튻ꆢ횤좯ퟩ뫏춶뗄뛠쒿뇪쟸볤쿟탔맦뮮쒣탍뗄붨솢 ꎨ튻ꎩMarkowitz붨솢뗄뺭뗤쒣탍 Harry .M. Markowitz쳡돶뗄횤좯ퟩ뫏춶뻹횵-랽닮쒣탍ꎬ튻횱놻톧쫵뷧릫죏캪쿖듺횤좯ퟩ뫏춶샭싛뗄믹쪯ꆣ뛸십뿋캬듄뗄쒣탍뗄샭싛잰쳡쫇붨솢퓚떥튻웚볤훐뫍훕뗣닆뢻킧펦뗄ퟮ듳뮯믹뒡횮짏ꆣ틲캪쫇떥튻웚볤ꎬ쯹틔쒣탍늻짦벰떽뢴샻ꎬ뛸훕뗣닆뢻킧펦뗄ퟮ듳뮯뇭쏷쒣탍볈뾼싇쇋닆뢻뗄ퟮ듳뮯ꎬ튲뾼싇떽쇋듦퓚뗄럧쿕ꎬ헢튲뻍쫇킧펦ퟮ듳뮯뗄몭틥ꆣ [1]Markowitz쒣탍캪ꎺ nmaxf(x)=Eꎨrꎩx∑iii=1nnσxx≤ω∑∑ijiji=1j=1 (3-1) n=∑ii=10≤x≤µ,=1,2",niiT웤훐x=(x,x,",x)뇭쪾횤좯ퟩ뫏ꎬr(i=1,2",n)뇭쪾뗚i훖횤좯돖폐웚12ninn뗄쫕틦싊ꎬE(r)(i=1,2",n)캪i훖횤좯돖폐웚뗄풤웚쫕틦ꎬσxx캪춶∑∑iijiji=1j=1Tퟩ뫏x=(x,x,",x)뗄랽닮ꎬ튻냣폃쯼뿉틔폃살뫢솿춶ퟩ뫏뗄럧쿕ꆣ12nσꎨi,j=1,2,",nꎩ뇭쪾뗚i훖횤좯뫍뗚j훖횤좯쫕틦싊뗄킭랽닮ꎬω캪춶헟쓜ij릻돐떣뗄럧쿕짏쿞ꎬµ(=1,2",n)캪춶뗚i훖횤좯뗄춶짏쿞ꆣ iMarkowitz뗄뻹횵-랽닮쒣탍틲캪듸폐뛾듎풼쫸ꎬ룸쪵볊펦폃쟳뷢듸살뫜듳삧쓑ꆣ뫳살뫜뛠톧헟뛔쒣탍뷸탐쇋룄뷸ꆣ퓚뻹횵-랽닮쒣탍훐ꎬ쫕틦싊뫍럧쿕튪쟳폃튻룶ힼ좷뗄쫽살뇭듯ꎬ떫쫇풤웚춶쫕틦싊뫍춶럧쿕놾살뻍쫇늻좷뚨뗄ꎬ뛸쟒춶헟웚췻뗄쫕틦튻냣쫇퓚튻룶랶캧쓚ꎬ쒣탍훐폃ힼ좷뗄쫽ퟖ뇭쪾늻뷶늻럻19
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 뫏쪵볊쟩뿶룼늻쓜쳥쿖돶춶헟뗄튻킩춶틢풸ꆣ쯦ퟅ쒣뫽쫽톧ꎬ쒣뫽뻶닟뗄랢햹ꎬ톧헟쏇붥붥틢쪶떽냑풤웚춶쫕틦싊뫍춶럧쿕폃쒣뫽쫽뗄탎쪽뇭쪾룼캪뫏샭ꆣ쿂쏦쫇뛔틽죫쟸볤쒣뫽쫽뗄횤좯춶ퟩ뫏뻹횵랽닮쒣탍뗄튻룶첽쳖ꆣ ꎨ뛾ꎩ쟸볤ퟩ뫏춶쒣탍뗄붨솢 −+짨쟸볤쫽r=[r,r]뇭쪾뗚i훖횤좯S퓚돖폐웚t쓚춶쫕틦뗄랶캧ꆣ횤좯춶itititiퟩ뫏뗄럧쿕퓲폃럧쿕쯰쪧싊살뫢솿ꆣ럧쿕쯰쪧싊쫇횸퓚튻룶춶훜웚쓚춶헟퓚랢짺럧쿕쪱뿉쓜뗄쯰쪧퓚ퟜ춶훐쯹햼뗄냙럖뇈ꆣ −+짨쟸볤쫽q=[q,q]뇭쪾뗚i훐횤좯S퓚돖폐웚t쓚뗄럧쿕쯰쪧싊뗄랶캧,xitititiit뇭쪾춶헟퓚돖폐웚t쓚뗚i훖횤좯S뗄춶뇈샽ꆣ틲캪맺쓚횤좯쫐뎡쿞훆싴뿕i뗄쟩뿶ꎬ쯹틔퓶볓풼쫸쳵볾x≥0ꆣ it퓚횤좯춶ퟩ뫏훐ꎬ춶헟ퟮ쾣췻뗄뻍쫇ퟩ뫏춶쫕틦뗄ퟮ듳뮯뫍ퟩ뫏춶럧쿕뗄ퟮ킡뮯ꆣ룹뻝듋튪쟳붨솢뛠쒿뇪쿟탔맦뮮쒣탍ꎺ nmaxR(x)=rx∑titi=1nmaxQ(x)=−qx (3-2) ∑titi=1nx=1,x≥0,∑i=1i1,2,",t=1,2,",m.뛾ꆢ횤좯춶뛠쒿뇪쒣뫽쟸볤쿟탔맦뮮쒣탍룄뷸 틲캪쒣뫽쿟탔맦뮮뒦샭뗄뢴퓓탔ꎬ뫜뛠톧헟뛔쟳쒣탍뗄쟳뷢랽램뷸탐쇋퇐뺿[6]뫍뒴탂ꆣ슷펦뷰ꎬ쳆킡컒ꎬ훜ퟚ럅퓚2004쓪퓚쟸볤쫽틑뺭뾪쪼듳솿펦폃폚룷훖쒣뫽뻶닟뗄믹뒡짏ꎬ붫쟸볤쫽룅쓮틽죫쇋횤좯ퟩ뫏춶쒣탍ꎬ늢쟒붨솢쇋믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍ꆣ춬쪱캪쇋뷢뻶펦폃컊쳢ꎬ춨맽틽죫뇭쪾춶헟뗄럧쿕쾲뫃돌뛈뗄럧쿕욫뫃쾵쫽α뗄랽램듓뛸붫쟸볤쫽뗄쿟탔맦뮮뇤캪닎쫽쿟탔맦뮮ꎬ뷢뻶쇋쟳뷢컊쳢ꎬ늢춨맽쪵횤횤쏷쇋쒣탍뗄쪵폃탔ꆣ 2007쓪ꎬ쇖뻼퓚웤싛컄ꆶ튻훖믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍폫쟳뷢ꆷ튻컄훐쳡돶ꎺ슷펦뷰뗈죋뗄쒣탍붫춶횤좯뗄풤웚쫕틦싊폫럧쿕쯰쪧싊짨훃돉쇋뛀솢뗄쟸볤쫽ꎬ뫶쫓쇋웤훐뗄듦퓚뗄쿠뮥맘쾵ꎬ폐뿉틔췪짆뗄뿕볤ꆣ늢쟒퓚싛컄훐20
뗚죽헂 쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍퇐뺿 [45]룸돶쇋룄뷸쒣탍ꆣ [46]돂맺뮪ꎬ돂쫕ꎬ췴쫙퇴퓚웤싛컄훐ꆶ쟸볤쫽쒣뫽춶ퟩ뫏쒣탍ꆷ훐ꎬ샻폃쇋쒣뫽풼쫸살볲뮯랽닮풼쫸ꎬ붫쒣탍뮯볲캪ꎺ nmaxf(x)=E(r)x∑iii=1nσx≤M+d(1−α)∑iii=1 (3-3) n=∑ii=10≤x≤µ,=1,2",nii웤훐α쫇춶헟뗄쒣뫽솥쫴뛈ꎬ0≤α≤1ꎬd캪춶죋뗄죝죌뛈ꎬσ쫇뗚i훖i럧쿕횤좯뗄뇪ힼ닮ꆣ웤쒣뫽늻뗈쪽뗄솥쫴몯쫽캪ꎺ 1,nM−σx∑iini=1µ(x)=,M−d≤σx≤M (3-4) ∑iidi=10ꎬ웤쯻붫3-3쪽뗄닎쫽쒣뫽쟸볤뮯뫳ꎬ뿉붫컊쳢뮯캪쿟탔맦뮮컊쳢ꆣ nmaxf(x)=[r,r]x∑iiii=1n[σ,]x≤[M+d(1−α),M+d(1−α)]∑iiii=1 (3-5) n=∑ii=10≤x≤µ,=1,2",nii뇊헟죏캪ꎬ돂맺뮪뗈죋퓋폃쒣뫽풼쫸살볲뮯Markowitz뗄M-V쒣탍뗄랽닮풼쫸ꎬ쯤좻뷢뻶쇋볆쯣짏뗄컊쳢ꎬ떫쫇쒣탍3-5짦벰떽Mꆢµꆢdꆢα쯄룶닎i쫽ꎬ헢킩닎쫽룹뻝쿖쪵훐뗄튻킩쟩뿶평뻶닟헟룸돶ꎬ퓚쪹뻶닟쒣탍룼죡탔뗄쟩뿶쿂튲믡뷸튻럅듳컳닮펰쿬뻶닟뗄늻ힼ좷탔ꆣ 2008쓪ꎬ돂뮪폑퓚웤돶냦뗄ꆶퟩ뫏풤닢랽램폐킧탔샭싛벰웤펦폃ꆷ튻쫩훐퓙듎ퟜ뷡룸돶쇋횤좯ퟩ뫏춶뗄뛠쒿뇪쟸볤쿟탔맦뮮쒣탍벰닉폃틽죫럧쿕욫뫃21
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 쾵쫽α뫍쒿뇪몯쫽폅뮯쮮욽닎쫽β뗄랽램ꎬ붫쒣탍뮯캪튻냣뗄닎쫽쿟탔맦뮮뷸탐쟳뷢ꆣ [41]틽죫닎쫽αꎨ0≤α≤1ꎩꎬ뿉붫3-2뮯캪떥쒿뇪쟸볤쿟탔맦뮮쒣탍 nnmaxZ(x)=αrx−(1−α)qx,∑∑titititit=1=1n (3-6) x=1,x≥0,∑i=1i=1,2,",n,t=1,2,",m,뫜쏷쿔ꎬ떱α=0ꎬ뇭쏷춶헟늻풸틢돐떣튻뗣럧쿕ꎬ튲벴튻룶벫뛋뗄럧쿕퇡뛱헟ꆣ떱α=1ꎬ뇭쏷춶헟횻맘탄샻틦늻퓚뫵돐떣럧쿕ꆣ쯹틔ꎬαퟷ캪럧쿕욫뫃닎쫽ꎬ뿉틔폃살뫜뫃뗄뫢솿춶헟뛔럧쿕뗄첬뛈ꆣ 붫3-6헻샭뇤탎죧쿂ꎺ nnmaxZ(x)=αrx−(1−α)qx,∑∑titititit=1=1nn−+−+α[r,r]x−(1−α)[q,q]x (3-7) ∑∑ititititititi=1=1n−++−[αr(1−α)q,αr−(1−α)q]x∑itititititi=1−+−++−쇮c=[c,c]=[αr(1−α)q,αr−ꎨ1-αꎩq],퓲쒣탍뮯캪 itititititititnmaxZ(x)=cx,∑titi=1n (3-8) x=1,x≥0,∑.i=1=1,2,",m.뛸춨맽틽죫쒿뇪폅뮯몯쫽폅뮯쮮욽뗄닎쫽βꎨ0≤β≤1ꎩ뗄랽램ꎬβ랴펳쇋춶헟뛔뷰죚쫐뎡뗄캴살ퟟ쫆뗄샖맛돌뛈ꆣ 붫β틽죫3-8ꎬ퓲쒣탍뿉틔뇤캪튻냣쿟탔맦뮮쒣탍ꎺ n+−maxZ(x)[βc(1−β)c]x∑tititi=1 (3-9) n+−−+{β[αr−(1α)q]+(1−β)[αr(1−α)q]}x∑itititititi=122
뗚죽헂 쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍퇐뺿 nx=1,x≥0,∑. i=1i1,2,",n,t=1,2,",m.샻폃튻냣쿟탔맦뮮뗄랽램뿉틔쟳돶ퟮ폅뷢ꎺ x(α,β)=(x(α,β),x(α,β),",x(α,β) t1t2tnt헢쫇냼몭α뫍β뗄쪹쒿뇪ퟮ폅뗄튻훖폐킧랽낸ꆣ떱α=0ꎬ뇭쏷춶헟늻풸틢돐떣튻뗣럧쿕ꎬ튲벴튻룶벫뛋뗄럧쿕퇡뛱헟ꆣ떱α=1ꎬ뇭쏷춶헟횻맘탄샻틦늻퓚뫵돐떣럧쿕ꆣ뛸β풽뾿뷼0ꎬ뇭쏷춶헟풽놯맛ꎬ랴횮ꎬβ풽뾿뷼1ꎬ뇭쏷춶헟풽쫇샖맛ꆣ 웤훐닎쫽α뫍β뿉틔룹뻝춶헟ퟔ짭뗄튪쟳살짨뚨ꆣ쿂쏦컒쏇붨솢쓜뇭듯β뫍α횮볤뗄맘쾵뗄몯쫽ꎬ틔뛔쒣탍뷸탐룄뷸ꆣ [47]뷼쓪살ꎬ튲폐톧헟죏캪럧쿕욫뫃쾵쫽α뫍쒿뇪몯쫽폅뮯쮮욽닎쫽β횮볤쫇듦퓚쒳훖맘쾵뗄ꆣ떱α듳뗄쟩뿶쿂ꎬβ튲믡뇈뷏듳닅뫏샭ꆣ쿠랴ꎬ떱α뷏킡뗄쟩뿶쿂ꎬβ뇈뷏킡닅뫏샭ꆣ웤훐틾몬뗄틢틥뻍쫇떱춶헟뛔뷰죚쫐뎡뗄ퟟ쫆뷏샖맛뗄ꎬ퓲춶헟뻍믡풸틢돐떣뷏듳럧쿕ꆣ 23
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 뗚쯄헂 쪵횤럖컶맽돌 튻ꆢ퇐뺿퇹놾폫퇹놾쫽뻝톡좡 룹뻝춶럖즢풭퓲뺡솿톡좡늻춬탐튵ꎬ늻춬돉뎤샠탍뗄20훖짏쫐릫쮾막욱ꎬ헢퇹벴ퟱ톭쇋럧쿕럖즢풭퓲튲쓜룼럻뫏튻냣춶헟뗄톡막쟩뿶ꎬ뿉틔뷸튻늽쳖싛쒣탍뗄쪵볊틢틥ꆣ 쫽뻝좡ퟔ2009쓪3퓂6죕-2010쓪3퓂5죕짏몣막욱붻틗쯹20훖막욱뗄52훜뗄훜튻뾪엌볛뫍훜컥쫕엌볛ꎬ쫽뻝쪹폃듳훇믛횤좯럖컶죭볾쿂퓘ꎬ쫽뻝볻뢽슼뇭Aꆣ 뛾ꆢ믹뒡쫽뻝뒦샭 ꎨ튻ꎩ막욱쫕틦싊뗄볆쯣 1ꆢ춶헟튪쟳뗄쫕틦싊볆쯣랽램 몺쒷쇐캬퓚웤훸ퟷꆶ춶톧ꆷ튻쫩훐횸돶폐죽훖볆쯣랽램뿉틔폃살볆쯣춶헟튪쟳뗄춶쫕틦싊ꎬ떱좻ꎬ헢샯뗄쫕틦싊쫇퓚좷뚨쟩뿶쿂춶헟튪쟳뗄튻룶뚨횵ꆣ [19]ꎨ1ꎩ막샻쳹쿖쒣탍맀볆램 d1k=+g (4-1) p0웤훐d뇭쪾퓚뗚튻쓪쒩횧뢶뗄쓪막샻ꎬp뇭쪾막욱볛룱ꎬg막샻퓶뎤싊ꆣ 10퓚릫쪽훐ꎬg튻냣쫇룶맀볆횵ꎬ틲캪쫐뎡뗄늻좷뚨탔벰럧쿕탔ꎬ쯹틔튻냣g믡놻뿌틢뗄뗍맀ꆣ틲뛸뎣뎣믡돶쿖g뇈만뚨쫕틦햮좯뗄만뚨쫕틦싊뮹뗍뗄쟩뿶ꆣ죧맻헢퇹ꎬ뻍쎻폐춶헟풸틢춶막샻퓶뎤싊죧듋횮뗍뗄막욱ꎬ릫쪽튲뻍쪧좥쇋쿖쪵틢틥ꆣ [19]ꎨ2ꎩ놾닺뚨볛쒣탍맀볆램 k=r+β[E(R)−r] (4-2) m웤훐r쫇컞럧쿕샻싊ꎬβ룹뻝뻟쳥쟩뿶살톡좡, E(R)쫇쫐뎡짏쯹폐막욱ퟩm24
뗚쯄헂 쪵횤럖컶맽돌 뫏뗄웚췻쫕틦싊ꆣ쿖퓚쪹폃듋릫쪽볆쯣쪱r,튻냣쪹폃뛌웚맺햮뗄샻싊살맀볆ꎬ헢퇹뿉틔붫풤웚춨믵엲헍뗄틲쯘뾼싇퓚쓚ꆣ [19]ꎨ3ꎩ샺쪷욽뻹쫽쯣램 샺쪷욽뻹쫽쯣램헢훖랽램쫇룹뻝웕춨막막샻쫕틦싊뗄샺쪷욽뻹쫽살맀볆춶헟튪쟳뗄쫕틦싊ꆣ헢훖랽램뗄샭싛룹믹쫇춶헟튪쟳믲헟쮵웚췻듯떽뗄쫕틦싊쫇욽뻹쫕틦싊뗄뷼쯆횵ꆣ [19]ꎨ4ꎩ뎤웚햮좯쫕틦싊맀볆램 뎤웚햮좯쫕틦싊맀볆램쫇샻폃쒳릫쮾뎤웚햮좯뗄떽웚쫕틦싊살맀볆춶헟튪쟳뗄쫕틦싊kꆣ튻냣쮵살ꎬ춶웕춨막뇈춶햮좯돐쫜룼듳뗄럧쿕ꆣ쯹틔볆쯣쪱튻냣믡퓚햮좯춶쫕틦싊뗄믹뒡짏볓짏4%ꎬ헢돆횮캪럧쿕놨돪싊ꆣ듋훖랽램닠훘폚뛔캴살뗄풤닢ꎬ틲캪퓚쪹폃릫쮾랢탐뗄뎤웚햮좯뗄쫕틦싊ퟷ캪춶뇪ힼ쪱ꎬ뎤웚햮좯쫕틦싊놾짭뻍냼삨쇋뛔쫐뎡뗄풤웚뫍뛔릫쮾잰뺰뗄풤닢ꆣ 뛸퓚쿖쪵훐ꎬ쿠뛔뛸퇔ꎬ쿖퓚샭닆쪦퓚샭닆맽돌훐룼뛠뗄쫇닉폃샺쪷욽뻹쫽[46]램살맀볆춶헟뗄풤웚쫕틦싊ꆣ컒쏇헢샯붫틔막욱뗄훜욽뻹쫕틦싊캪닎뾼ꎬ살좷뚨막욱뗄풤웚쫕틦싊ꎬ퓚헢샯틲캪컒맺뫜짙럖엤막욱막샻ꎬ쯹틔볆쯣훐늻뾼싇ꎬ좻뫳틔듋캪틀뻝붨솢뫏샭뗄쫕틦쟸볤ꆣ [48,19]2ꆢ막욱훜쫕틦싊볆쯣랽램 p−pitit−1r= (4-3) itpit−1r쫇막욱i퓚뗚t훜뗄쫕틦싊ꎬi=1,2,3 ",=1,2,3 "52; itp쫇막욱i퓚뗚t훜웚쒩뗄볛룱ꎬ볆쯣쪱튻냣톡폃뗚t훜훜컥쫕엌볛볆쯣ꎻ itp쫇막욱i퓚뗚t훜웚돵뗄볛룱,볆쯣쪱튻냣톡폃뗚t훜훜튻뗄뾪엌볛볆쯣ꆣ it−1ꎨ뛾ꎩ막욱뗄럧쿕볆쯣 Markowitz뗄닺ퟩ뫏샭싛훐ꎬ폃횤좯춶쫕틦싊뗄랽닮살에뛏횤좯쫐뎡럧쿕뗄듳킡ꎬ뻹횵-랽닮쒣탍튲쫇붨솢퓚듋볙짨뗄믹뒡짏ꆣ헢튻볙짨퓚뫜뎤뛎쪱볤쓚쫜떽뫜뛠톧헟뗄훊틉ꎬ뇈죧킭랽닮뗄볆쯣컊쳢뗈뗈ꆣ쿖퓚ꎬ톧쫵뷧웕뇩죏캪ꎺ떱쪵볊쫕틦뗍폚풤웚쫕틦쪱ꎬ뻍믡닺짺쯹캽뗄럧쿕ꆣ튻룶폐폃뗄믲헟쮵폐볛횵뗄럧쿕닢뛈펦룃쫇쒳훖ꆰ뮵ꆱ뗄쟩뿶뗄뛈솿ꆣ뇪ힼ닮σ뻍쫇튻룶맀볆쪵볊쫕틦싊폫25
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 풤웚쫕틦싊횮볤욫닮뗄럧쿕닢뛈횵ꆣ퓚춶샭닆훐ꎬ춶럧쿕놻뚨틥캪쪵볊쫕틦욫샫풤웚쫕틦뗄뿉쓜탔ꎬ욫샫뗄풽듳ꎬ퓲죏캪럧쿕폺듳ꆣ 1ꆢ룅싊쳵볾쿂떥룶횤좯풤웚쫕틦싊랽닮볆쯣릫쪽 n22σp[r−Eꎨrꎩ] (4-4) ∑iii=12웤훐σ쫇풤웚쫕틦싊랽닮ꎬr캪횤좯뿉쓜돶쿖뗄뗚i훖풤웚쫕틦싊ꎬp쫇r랢iii짺뗄룅싊ꎬEꎨrꎩ캪횤좯뗄풤웚쫕틦싊ꎬσ캪풤웚쫕틦싊뗄뇪ힼ닮ꆣ랽닮믲헟뇪ힼ닮풽듳ꎬ럧쿕뻍풽듳ꆣ 떫쫇4-4볆쯣쪱듦퓚뫜듳컊쳢ꎬ뻍쫇p뗄늻뿉풤닢탔튲벴늻뿉횪탔ꆣ i2ꆢ룹뻝퇹놾뿕볤죝솿볆쯣떥횻막욱쫕틦싊랽닮릫쪽 N2(r−r)∑i2i=1σ= (4-5) N−1r캪맛달횵뗄욽뻹횵ꎬN캪쫕틦싊맛달횵뗄쫽솿ꆣ ꎨ죽ꎩ쫽뻝뒦샭뷡맻 [49]쪹폃Excel뗄몯쫽볆쯣릦쓜,틀뻝릫쪽4-3뫍4-5볆쯣돶쯹톡막욱퓚2009쓪3퓂6죕떽2010쓪3퓂5죕52훜쓚뗄훜쫕틦싊ꎬ퓙뻝듋쯣돶20횻막욱뗄욽뻹훜쫕틦싊뫍뇪ힼ닮ꆣ쫽뻝죧뇭4-1쯹쪾ꎺ 뇭4-1 욽뻹쫕틦싊뫍뇪ힼ닮볆쯣맽돌뇭 막욱 췲뿆A 훐맺욽낲 훐맺쪯폍 훐탋춨톶헐짌틸탐춭쇪폐즫뺩뚫랽ꏁ짏몣뗧솦 냼룖쾡췁맺뗧쓏ퟔ훜쫽 훜쫕틦싊 훜쫕틦싊 훜쫕틦싊 훜쫕틦싊훜쫕틦싊훜쫕틦싊훜쫕틦싊훜쫕틦싊 훜쫕틦싊훜쫕틦싊1 2 3 4 5 6 7 26
뗚쯄헂 쪵횤럖컶맽돌 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 27
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 뻹횵 σ i막욱 짏몣볒뮯 쯄뒨뎤뫧 냙듳벯췅 훐벯벯췅탬릤믺킵죊뫍튩튵뗧맣뒫쎽럡풭짺뮯 쓏 뺩 룛좫 뻛 뗂훜쫽 훜쫕틦싊 훜쫕틦싊 훜쫕틦싊 훜쫕틦싊훜쫕틦싊훜쫕틦싊훜쫕틦싊훜쫕틦싊 훜쫕틦싊훜쫕틦싊1 2 3 4 5 6 7 8 28
뗚쯄헂 쪵횤럖컶맽돌 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 29
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 뻹횵 σ i 죽ꆢ쫕틦쟸볤뫍럧쿕쟸볤좷뚨 뷼쓪살ꎬ톧헟뛔믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍뗄퇐뺿돉맻뷏뛠ꎬ떫쫇듳뛠벯훐퓚쫽톧쇬폲ꎬ뛔폚쪵폃탔뫍뿉폃탔뗄퇐뺿뷏짙짵훁쫇튻뇊듸맽ꆣ쳘뇰쫇뫳웚쫽뻝뒦샭쪱ꎬ뛔폚쫕틦쟸볤믲헟럧쿕쟸볤뗄좷뚨ꎬ쎻폐틀뻝쿖폐샭싛짮죫퇐뺿틔쳡룟쒣탍뗄쪵폃탔ꆣ놾컄붫룹뻝쿖폐뗄컄쿗ꎬ톡좡튻훖뫏샭뗄뿆톧랽램살좷뚨쟸볤ꆣ ꎨ튻ꎩ쫕틦쟸볤좷뚨 [42]폐톧헟쳡돶ꎬ컒쏇뿉틔룹뻝뻉뗄쫕틦싊살맀볆캴살쫕틦싊ꆣ놾컄톡퓱쇋횸쫽욽뮬램살풤닢횤좯뗄풤웚쫕틦싊벰랶캧ꎬ늢쟒룸돶쇋펦폃횸쫽욽뮬랽램뗄뻟쳥쯣샽ꆣ 횸쫽욽뮬램볆쯣릫쪽죧쿂ꎺ 30
뗚쯄헂 쪵횤럖컶맽돌 ˆˆr=αr+(1−α)ri+1iiRrˆ= (4-6) FN+1r+r12ˆr=12웤훐R뇭쪾횤좯뗄풤웚쫕틦싊ꎬα뇭쪾볓좨쾵쫽ꎨ0≤α≤1ꎩꆣα뿉틔룹뻝Fퟔ벺뛔쇩쏴뛈뗄튪쟳믲헟횮잰뗄쫕틦싊뗄뇤뮯쇩쏴뛈살톡좡ꆣ퓚헢샯ꎬ컒쏇룹뻝뇭1훜쫕틦싊쫽뻝뷏캪욽컈뗄뻟쳥쟩뿶톡퓱α=ꆣ 샻폃Excel훐뗄몯쫽볆쯣릦쓜ꎬ룹뻝4-6폃52훜쫕틦싊볆쯣돶풤닢쫕틦싊RꎬF쫽뻝볻뇭4-2ꎺ 뇭4-2 막욱풤웚쫕틦싊뇭 횤좯쏻돆 췲뿆A 훐맺욽낲 훐맺쪯폍 훐탋춨톶 헐짌틸탐 R 횤좯쏻돆 춭쇪폐즫 뺩뚫랽ꏁ 짏몣뗧솦 냼룖쾡췁 맺뗧쓏ퟔ R 횤좯쏻돆 짏몣볒뮯 쯄뒨뎤뫧 냙듳벯췅 훐벯벯췅 탬릤믺킵 R 횤좯쏻돆 죊뫍튩튵 뗧맣뒫쎽 럡풭짺뮯 쓏 뺩 룛 좫 뻛 뗂 R [48]룹뻝컄쿗ꎬ쪹폃횸쫽욽뮬랽램볆쯣돶살뗄풤웚쫕틦싊뗄뇤뮯랶캧쫇R-σ,R+σꎬ틀뻝듋릫쪽폃뇭4-1뫍뇭4-2뗄쫽뻝볆쯣돶20훖막욱뗄풤웚쫕[]FF틦쟸볤ꎺ 뇭4-3 막욱풤웚쫕틦쟸볤뇭 횤좯쏻돆 췲뿆A 훐맺욽낲 훐맺쪯폍 훐탋춨톶 헐짌틸탐 [ꎬ [ꎬ [ꎬ [ꎬ [ꎬ −+[r,r] ] ] ] ] ] 횤좯쏻돆 춭쇪폐즫 뺩뚫랽ꏁ 짏몣뗧솦 냼룖쾡췁 맺뗧쓏ퟔ 31
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 [ꎬ [ꎬ [ꎬ [ꎬ [ꎬ −+[r,r] ] ] ] ] ] 횤좯쏻돆 짏몣볒뮯 쯄뒨뎤뫧 냙듳벯췅 훐벯벯췅 탬릤믺킵 [ꎬ [ꎬ [ꎬ [ꎬ [ꎬ −+[r,r] ] ] ] ] ] 횤좯쏻돆 죊뫍튩튵 뗧맣뒫쎽 럡풭짺뮯 쓏 뺩 룛 좫 뻛 뗂 [ꎬ [ꎬ [ꎬ [ꎬ [ꎬ −+[r,r] ] ] ] ] ] ꎨ뛾ꎩ럧쿕쟸볤좷뚨 −+−+짨R=[r,r]ꎬQ=[q,q]ꎬ웤훐R뇭쪾퓚돖폐웚t쪱볤쓚뗚i훖럧쿕횤좯ititititititit뗄풤웚쫕틦싊랶캧ꎬQ뇭쪾뗚i훖럧쿕횤좯퓚돖폐웚t쪱볤뗄럧쿕쯰쪧싊랶캧ꆣ it[42]뇪ힼ닮σ쫇횸럧쿕횤좯뗄쫕틦싊뛔웤풤웚쫕틦싊뗄뿉쓜욫샫돌뛈ꎬ톧쫵i뷧웕뇩죏캪뇪ힼ닮뿉틔ퟷ캪럧쿕뫢솿뗄횸뇪ꆣ떫쫇쿖쪵훐뗄럧쿕늢늻쫇튻룶좷뚨횵ꎬ뛸쟒춶헟풸틢돐쫜뗄럧쿕웤쪵튲쫇튻룶쟸볤ꆣ쯹틔퓚믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍훐ꎬퟛ뫏춶헟뗄탄샭뗈룷훖틲쯘ꎬ 틀뻝뇭1훐뗄뇪ힼ닮σ횵ꎬ컒i쏇톡좡 σ±맀볆돶튻룶쟸볤ퟷ캪쒣탍뗄럧쿕쟸볤ꎺ i뇭4-4 막욱럧쿕쟸볤뇭 횤좯쏻돆 췲뿆A 훐맺욽낲 훐맺쪯폍 훐탋춨톶 헐짌틸탐 [ꎬ [ꎬ [ꎬ [ꎬ [ꎬ −+[q,q] ] ] ] ] ] 횤좯쏻돆 춭쇪폐즫 뺩뚫랽ꏁ 짏몣뗧솦 냼룖쾡췁 맺뗧쓏ퟔ [ꎬ [ꎬ [ꎬ [ꎬ [ꎬ −+[q,q] ] ] ] ] ] 횤좯쏻돆 짏몣볒뮯 쯄뒨뎤뫧 냙듳벯췅 훐벯벯췅 탬릤믺킵 [ꎬ [ꎬ [ꎬ [ꎬ [ꎬ −+[q,q] ] ] ] ] ] 횤좯쏻돆 죊뫍튩튵 뗧맣뒫쎽 럡풭짺뮯 쓏 뺩 룛 좫 뻛 뗂 32
뗚쯄헂 쪵횤럖컶맽돌 [ꎬ [ꎬ [ꎬ [ꎬ [ꎬ −+[q,q] ] ] ] ] ] 쯄ꆢ쒣탍뗄맦뮮쟳뷢 룹뻝뇭4-3뫍뇭4-4뗄쫽뻝내헕릫쪽3-9붨솢횤좯ퟩ뫏춶쟸볤쫽쿟탔맦뮮쒣탍ꎺ 20+−−+maxZ(x){β[αr−(1α)q]+(1−β)[αr(1−α)q]}x ∑titititititi=1x+x+"x=1 (4-7) x≥0,i=1,2"20.it짨ꎨα=0ꎬβ=0ꎩꎬꎨα=0, β=ꎩ,ꎨα=0, β=ꎩꎬꎨα=0, β=1ꎩꎬꎨα=, β=ꎩ,ꎨα=ꎬβ=ꎩ,ꎨα=ꎬβ=ꎩ,ꎨα=ꎬβ=ꎩ,ꎨα=ꎬβ=1ꎩ,ꎨα=1ꎬβ=1ꎩ,룹뻝듋쫽횵듺죫4-7쪽볆쯣럧쿕횤좯뗄춶럝뛮ꆣ 컥ꆢ쪵횤퇐뺿뷡맻 [50]닉폃lingo죭볾뇠돌뛔쫽뻝뷸탐럖컶ꎬ룹뻝늻춬뗄αꎬβ횵ꎬ뗃돶횤좯춶ퟩ뫏뗄ퟮ병돖막뇈샽ꎬ뷡맻죧뇭4-5ꎺ 뇭4-5 쪵횤퇐뺿뷡맻뇭 α 0 0 0 0 β 0 1 막욱쏻돆 돖막뇈샽 돖막뇈샽 돖막뇈샽 돖막뇈샽 돖막뇈샽 췲뿆A 0 0 0 0 훐맺욽낲 0 0 0 0 훐맺쪯폍 0 0 훐탋춨톶 0 0 0 0 33
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 헐짌틸탐 0 0 0 0 0 춭쇪폐즫 0 뺩뚫랽ꏁ 0 0 짏몣뗧솦 0 냼룖쾡췁 0 0 0 0 맺뗧쓏ퟔ 0 0 0 짏몣볒뮯 0 0 0 0 0 쯄뒨뎤뫧 0 0 냙듳벯췅 0 0 훐벯벯췅 0 0 0 0 0 탬릤믺킵 0 0 0 죊뫍튩튵 0 0 뗧맣뒫쎽 0 0 0 럡풭짺뮯 0 쓏 뺩 룛 0 0 0 좫 뻛 뗂0 0 0 0 0 쒿뇪몯쫽 α 1 β 1 1 막욱쏻돆 돖막뇈샽 돖막뇈샽 돖막뇈샽 돖막뇈샽 돖막뇈샽 췲뿆A 0 0 0 0 34
뗚쯄헂 쪵횤럖컶맽돌 훐맺욽낲 0 0 0 0 훐맺쪯폍 0 훐탋춨톶 0 0 0 0 0 헐짌틸탐 0 0 0 0 0 춭쇪폐즫 0 0 0 뺩뚫랽ꏁ 0 0 0 짏몣뗧솦 0 0 0 0 냼룖쾡췁 0 0 0 맺뗧쓏ퟔ 0 0 0 0 짏몣볒뮯 0 0 0 0 쯄뒨뎤뫧 0 0 0 0 냙듳벯췅 0 0 0 0 0 훐벯벯췅 0 0 0 0 탬릤믺킵 0 0 0 0 죊뫍튩튵 0 0 뗧맣뒫쎽 0 0 0 럡풭짺뮯 0 쓏 뺩 룛0 0 0 0 좫 뻛 뗂0 0 0 0 쒿뇪몯쫽 평뇭4-5뿉틔뾴돶ꎬα뫍β폫쒿뇪몯쫽횵듦퓚튻뚨맘쾵ꎬα풽듳ꎬβ풽듳퓲쒿뇪몯쫽튲쿠펦뗄퓶듳ꎬ뛸떱α풽킡ꎬβ풽킡쪱ꎬ쒿뇪몯쫽튲풽킡ꆣ튲뻍쫇쮵쒿35
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 뇪몯쫽ꎨ쫕틦뫍럧쿕뗄좨뫢뗄ퟮ듳횵ꎩ쫇α뫍β뗄퓶몯쫽ꆣ쒣탍쪹춶럖컶룼뻟폐죡탔ꎬ춶헟뿉틔틀뻝ퟔ벺뛔뿍맛쟩뿶뗄에뛏ꎬ뗃떽쫊뫏ퟔ벺춶욫뫃뗄춶ퟩ뫏뻶닟랽낸ꆣ 36
뗚컥헂 뷡싛ꆢ늻ퟣ뫍햹췻 뗚컥헂 뷡싛ꆢ늻ퟣ뫍햹췻 춶ퟩ뫏샭싛ꎬ믲헟룼맣랺뗄쮵뷰죚춶샭싛ꎬ틑뺭돉캪쿖듺뷰죚퇐뺿랢햹퇐뺿뗄훷쿟ꆣ쿖퓚ꎬ춶ퟩ뫏샭싛놻죏캪쫇쿖듺뷰죚톧뗄뫋탄컊쳢횮튻ꎬ뛔웤샭싛랽램뗄퇐뺿뿉틔쮵벫폐솦뗄췆뚯쇋쿖듺뷰죚톧뗄랢햹ꎬ폫춶ퟩ뫏쏜쟐쿠맘뗄룷훖퇐뺿돉맻ꎬ늻뛏볓짮ퟅ죋쏇뛔쿖듺뷰죚뗄죏쪶ꆣ춶ퟩ뫏톡퓱뺭맽50뛠쓪뗄랢햹ꎬ웤퇐뺿뫍쪵볹틑뺭좡뗃쇋쿠떱럡뢻뗄돉맻ꆣ 뷼쓪살ꎬ쯦ퟅ뷰죚뫍ퟮ폅뮯샭싛폫랽램뗄랢햹ꎬ춶ퟩ뫏훷튪벯훐퓚퇐뺿죧뫎붨솢룷훖럻뫏뻶닟헟튪쟳뗄쒣탍ꎬ뛔폚쒣탍뗄쟳뷢랱쯶컊쳢ꎬ뫜뛠톧헟훂솦폚퇐뺿쒣탍뗄폐킧쯣램ꎬ쳡돶쇋듳솿뗄웴랢쪽쯣램ꎬ쯦ퟅ쿟탔맦뮮죭볾뗄늻뛏랢햹췪짆ꎬ퇐뺿죧뫎붨솢뿉뮯캪쿟탔맦뮮뗄횤좯춶ퟩ뫏쒣탍ꎬ뛔컒쏇뗄쪵볊쟳뷢뻟폐훘튪뗄톧쫵틢틥뫍쪵폃틢틥ꆣ 놾컄쳡돶쇋튻훖믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍ꎬ쒣탍쫇붨솢퓚Markowitz뻹횵-랽닮쒣탍뗄믹뒡짏뗄ꆣ퓚Markowitz뗄뻹횵-랽닮쒣탍훐ꎬ쫕틦싊뫍럧쿕쫇폃튻룶ힼ좷뗄쫽살뇭듯ꎬ떫쫇쿖쪵훐뗄쟩뿶쫇풤웚춶쫕틦싊뫍춶럧쿕놾살뻍뻟폐뫜듳뗄늻좷뚨뗄ꎬ뛸쟒춶헟웚췻뗄쫕틦튻냣튲쫇퓚튻룶랶캧쓚ꎬ늻쫇튻룶ힼ좷뗄쫽ꎬ쯹틔Markowitz뻹횵-랽닮쒣탍훐폃ힼ좷뗄쫽ퟖ뇭쪾늻뷶늻럻뫏쪵볊쟩뿶룼늻쓜쳥쿖돶춶헟뗄튻킩춶틢풸ꆣ놾싛컄훐냑풤웚춶쫕틦싊뫍춶럧쿕폃쒣뫽쟸볤쫽뗄탎쪽뇭쪾ꎬ늢쟒닉폃쇋쪱볤탲쇐쒣탍훐뗄횸쫽욽뮬풤닢램좷뚨풤웚쫕틦쟸볤ꎬ좻뫳춨맽틽죫쟸볤쒣뫽쫽뗄횤좯춶ퟩ뫏뻹횵랽닮쒣탍붫뛔춨맽틽죫럧쿕욫뫃쾵쫽α뫍쒿뇪몯쫽폅뮯쮮욽닎쫽β뗄랽램ꎬ붫웤뮯캪쟸볤쫽뛠쒿뇪쿟탔맦뮮컊쳢뷸탐쟳뷢ꆣ럧쿕욫뫃쾵쫽α뫍쒿뇪몯쫽폅뮯쮮욽닎쫽β뿉틔룹뻝ퟔ벺뛔춶럧쿕뗄욫뫃돌뛈뫍뛔캴살춶쫐뎡뗄맀볆돌뛈룸돶ꎬ뛸룹뻝2009쓪3퓂6죕-2010쓪3퓂5죕짏몣막욱붻틗쯹20훖막욱뗄52훜뗄훜튻뾪엌볛뫍훜컥쫕엌볛닉폃횸쫽욽뮬램룹뻝룸돶풤웚쫕틦싊쟸볤ꎬ퓚볦맋춶뻶닟죡탔뮯뗄믹뒡짏ꎬ튲퓚쫽뻝뗄뒦샭짏룼뻟폐뿆톧탔늢쟒볦맋쇋뿍맛쫂쪵ꆣ쿠탅듋뻶닟쒣탍컞싛퓚죕틦랢햹뗄춶샭닆쫐뎡뮹쫇퓚믹뷰톡막훐ꎬ뚼믡웰떽훘튪뗄닎뾼ퟷ폃ꆣ 놾싛컄퓚쿞훆싴뿕뗄잰쳡쿂퓚뛔튻훖믹폚쟸볤쫽뛮횤좯춶ퟩ뫏쒣탍뷸탐37
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 쪵횤럖컶ꎬ붫웤뮯돉쟸볤쫽뛠쒿뇪쿟탔맦뮮컊쳢뷸탐쟳뷢ꎬ횤쪵쇋웤뫏샭탔뫍폐킧탔ꆣ떫쫇틲캪쪱볤폐쿞ꎬ쮮욽폐쿞ꎬ뮹폐뿉틔췪짆뗄뿕볤ꆣ컒죏캪틔뫳쟸볤쫽춶ퟩ뫏쒣탍뗄퇐뺿랽쿲펦룃훷튪벯훐퓚틔쿂벸뗣ꎺ 1ꆢ뾼싇떽붻틗럑폃뗄춶ퟩ뫏컊쳢뗄퇐뺿ꆣ놾싛컄횻뾼싇떽쇋맺쓚횤좯붻틗쫐뎡쿞훆싴뿕뗄잰쳡쳵볾ꎬ늢쎻폐뾼싇폫붻틗솿돉뇈샽뗄붻틗럑폃ꆣ뛸퓚쪵볊뗄뷰죚쫐뎡ꎬ웤쪵쫇듦퓚ퟅ뫜뛠탎쪽뗄붻틗럑폃뗄ꎬ룷훖탎쪽뗄붻틗럑폃뚼뿉쓜믡뛔춶ퟩ뫏톡퓱폐ퟅ횱뷓뗄펰쿬ꆣ뿉쫇평폚붻틗럑폃뗄뛠퇹탔뫍뢴퓓탔ꎬ쪹뗃뾼싇떽붻틗럑폃뗄쟸볤쫽횤좯춶ퟩ뫏쒣탍붨솢늻뷶폐튻뚨뗄삧쓑ꎬ튲퓚튻킩랽쏦욫샫쪵볊ꎬ폈웤쫇퓚붫쫕틦뫍럧쿕뚼짨캪쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍훐ꎬ죧맻뾼싇떽횤좯뗄붻틗럑폃붫믡쪹쒣탍뗄붨솢뫍쟳뷢뚼룼볓뢴퓓ꎬ쯹틔쮵헢붫믡쫇틔뫳톧쫵퇐뺿뗄튻룶훘튪랽쿲ꆣ 2ꆢ놾컄쳡돶뗄쟸볤쒣뫽쫽춶ퟩ뫏쒣탍쫇뺲첬쳵볾쿂붨솢뗄횤좯춶ퟩ뫏쒣탍ꎬ뛸쪵볊뗄춶맽돌튻냣죏캪쫇뚯첬믲헟뿉틔쮵쫇퓚튻뛎쪱볤쓚튻룶돖탸믲헟훘뢴뗄맽돌ꆣ뛸쟒ꎬ쒿잰뗄뛠뷗뛎뚯첬춶ퟩ뫏컊쳢뗄퇐뺿죔좻폫춶훐뗄헦쪵쟩뿶쿠닮짵풶ꎬ퓚쒣뫽뮷뺳쿂붨솢뛠웚춶ퟩ뫏뻶닟쒣탍뻟폐뷏듳뗄퇐뺿틢틥뫍뷏듳퇐뺿뿕볤ꆣ뿉틔쮵ꎬ붫뛠웚뗄룅쓮틽죫쟸볤쒣뫽쫽횤좯춶ퟩ뫏컊쳢붫쫇뷱뫳튻룶훘튪뗄퇐뺿랽쿲ꆣ 3ꆢ뾼싇떽쇷뚯탔뗄횤좯춶ퟩ뫏쒣탍튲붫믡쫇틔뫳뗄튻룶퇐뺿훘뗣ꎬ횮잰튲폐톧헟붫뮻쫖싊짨캪튻룶쟸볤쫽ퟷ캪뫢솿쇷뚯탔뗄횸뇪틽죫쟸볤쫽춶ퟩ뫏맦뮮쒣탍ꎬ떫쫇뷏캪잣잿ꆣ쇷뚯탔믲헟쮵뮻쫖싊튲쫇횤좯춶쪱탨튪훘뗣뾼싇뗄컊쳢ꎬ쯹틔쮵퓚헢랽쏦뮹폐횵뗃짮죫퇐뺿뗄뿕볤ꆣ 38
닎뾼컄쿗 닎뾼컄쿗 [01]William F Sharpe.횤좯춶풭샭[M].퇮탣첦,쇵탇뗈뇠틫.훘쟬ꎺ훘쟬듳톧돶냦짧,1998:86-97. [02]Markowitz H M., Portfolio selection [J]. Journal of Finance,1952,7:77-91. [03]Sharp W F. Portfolio theory and capital market[J] .New YorkꎺMcGraw-Hill, 1970:32-40. [04]Lintner valiation of risk assets and the selection of risky investments in stock portfolios and capital budgets[J]. Review of Economics and Statistics,1965,47: 13-37. [05]Ross S. A mutual funds separation in financial theory-The Separating Distributions [J]. Journal of Economic Theory,1978,17:24-36. [06]슷펦뷰,쳆킡컒,훜ퟚ럅.횤좯ퟩ뫏춶뗄쟸볤쫽쿟탔맦뮮랽램[J].쾵춳릤돌톧놨,2004,19(1):33-37. [07]Mao J C T.ꎬModels of capital budgeting. E-V vs E-S [J]. Journal of Financial And Quantitative Analysis,1970,5:657-675. [08]Konno H. Piece wise linear risk functions and portfolio optimization [J]. Journal of the Operations Research Society of Japan,1990,l33(2):139-156. [09]Alexander G. J. Short selling and efficient sets[J] .Journal of Finance,1993, 48:1497-1560. [10]Xia Yusen,Liu B D,Wang S Y. A model portfolio selection with order of expected returns[J].Computers & Operations Research,2000,27:409-422. [11]Li zhongfei,Wang S Y, Deng X T. A linear programming algorithm for optimal portfolio selection with transaction costs[J].International Journal of systems Science,2000,31(l):107-117. [12]Konno H,Waki H,Yuuki. A portfolio optimization under-lower partial risk measures [J]. Asia-Pacific Financial Markets,2002,9:127-140. [13]Black F. Capital market equilibrium with restricted borrowing[J] .Journal of Business,1972,45(3):444-454. [14]Fama E. Multiperiod consumption-investment decision[J].American 39
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 Economic Review,1970,60ꎨ1ꎩ:163-174. [15]Merton R intertemporal capital asset pricing model[J] .Econmetrica, 1973, 41(5):867-887. [16]Levy H,Samuelsen P capital asset pricing model with diverse holding periods[J].Management Science,1992,38(11):1529-1542. [17]Marshall J F,Bansal V K.뷰죚릤돌[M].쯎럪쏷뗈틫.놱뺩ꎺ쟥뮪듳톧돶냦짧,1999:137-147. [18]Zhou ,Li time mean-variance portfolio selection:A Stochastic LQ framework[J].Applied Math&OPT,2000,42:19-33ꎬ [19]몺쒷.쇐캬춶톧[M].죎뮴탣뗈틫.놱뺩:놱뺩듳톧돶냦짧,2000:267-289. [20]Fama E. Efficient capital market markets:A review of theory and empirical work[J]. Journal of Finance,1970,25(2):383-417. [21]Berk J B,Green R C,Naik V. Optimal options and security returns[J].Journal of Finance,1999,54(5):1553-1607. [22]퓸폂,쳆킡컒.쿞훆싴뿕쟩뿶쿂ퟩ뫏횤좯폐킧뇟뷧뗄쳘헷뫍좷뚨랽램[J].맜샭릤돌톧놨ꎬ1997,11ꎨ3ꎩꎺ147-154. [23]십폀뾪ꎬ쳆킡컒.싴뿕폫횤좯ퟩ뫏춶[J].풤닢,1999,1:35-42. [24]십폀뾪ꎬ쳆킡컒.늻퓊탭싴뿕뗄β횵횤좯ퟩ뫏춶뻶닟쒣탍퇐뺿[J].맜샭릤돌톧놨ꎬ1999,4ꎺ21-27. [25]퓸폂ꎬ쳆킡컒ꎬ횣캬쏴.믹뷰럖샫뚨샭뗄뷸튻늽퇐뺿[J].쾵춳릤돌톧놨,2001,16(3):187-191. [26]역량ꎬ볖붨쏱ꎬ믆뗇쫋.튻룶벫듳벫킡럧쿕볛횵뗄ퟩ뫏춶쒣탍[J].쾵춳릤돌샭싛랽램펦폃,2004,13(4):350-354. [27]샮톡뻙ꎬ룟좫쪤.붻틗럑폃뫍CVaR럧쿕닢뛈쿂뗄컈붡춶ퟩ뫏[J].쫽솿뺭볃벼쫵뺭볃퇐뺿,2004:85-90. [28]역듳뫢ꎬ튦풪뛋.듸믺믡풼쫸뗄뚯첬춶뻶닟쒣탍퇐뺿[J].훐맺맜샭뿆톧ꎬ2005,13(1):9-13. [29]훬쫩짐.뛠뷗뛎춶ퟩ뫏톡퓱벰웤럧쿕뿘훆[D].놱뺩ꎺ훐뿆풺쫽톧폫쾵춳뿆톧퇐뺿풺늩쪿톧캻싛컄,2003:12-32. 40
닎뾼컄쿗 [30]돂뮪폑ꎬ헔폱쎷.믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍퇐뺿[J].듳톧쫽톧,2007,23(1):11-15. [31]Zadeh L A. Fuzzy sets[J].Information and Control,1965,8:338튻353. [32]Bellman R,Zadeh L A. Decision making in a fuzzy environment Science[J]. Management Science,1970,17:141-164. [33]Kwakernaak H. Fuzzy random variables [J]. Information Science,1978, 15(1):65-72. [34] Ramaswamy S. Portfolio selection using fuzzy decision theory[J]. Working Paper of Bank for International Settlements,1998, 59:101-110. [35]폚펢뒨.쿖듺뻶닟샭싛폫쪵볹[M].놱뺩ꎺ뿆톧돶냦짧,2005:13-35. [36]C W Churchman,R L Ackoff,E L Arnoff. Introduction to operations research [J].Wiley,New York,1957:86-98. [37]K R MacCrimmon,J L Zeleny M .An overview of multiple objectives decision making cochrance multiple criteria decision [J].Columbia South Carolina: University of South Carolina Press,1973:18-44. [38]C L Hwang,K S Yooh. Multiple attribute decision making-method and application[J].New York:Springer-Verlay,1981:23-51. [39]탬뻁욽ꎬ샮뻼.뛠쒿뇪뻶닟뗄샭싛폫랽램[M].놱뺩ꎺ쟥뮪듳톧돶냦짧, 2005:2-21. [40]컢뇼볡.쒣뫽쫽톧벰웤뺭볃럖컶[M].놱뺩:훐맺뇪ힼ돶냦짧,1994:23-55. [41]돂뮪폑.ퟩ뫏풤닢랽램폐킧탔샭싛벰웤펦폃[M].놱뺩ꎺ뿆톧돶냦짧, 2008:215-218. [42]쇵킡쇡.횤좯춶풤웚쫕틦싊폫럧쿕뗄뛈솿랽램[J].춳볆폫뻶닟,2005,4:30-32. [43]췀탂쫯.횤좯뗄럧쿕뛈솿쒣탍폫ퟩ뫏춶폅뮯샭싛[J]훐맺닆헾뺭볃돶냦짧ꎬ2003:21-28. [44]Box G E P,Jenkins G M,Reninsel G C.쪱볤탲쇐럖컶ꎺ풤닢폫뿘훆[M].맋훷틫.놱뺩ꎺ훐맺춳볆돶냦짧,1997:211-376. [45]쇖뻼.튻훖믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍폫쟳뷢[J].쫽톧뗄쪵볹폫죏41
믹폚쟸볤쫽뗄횤좯춶ퟩ뫏쒣탍뫍쪵횤퇐뺿 쪶,2007,37ꎨ23ꎩ:1-7. [46]돂맺뮪ꎬ돂쫕ꎬ췴쫙퇴.쟸볤쫽쒣뫽춶ퟩ뫏쒣탍[J].쾵돌릤돌,2007, 25(8):34-37. [47]쇎킡솬ꎬ돂맺뮪.믹폚β풼쫸뗄쒣뫽춶ퟩ뫏쒣탍[J].훐맺뺭볃폫맜샭뿆톧,2008ꎬ12(8):154-155. [48]슬톧램.횤좯춶믹뷰벨킧움볛쪵횤퇐뺿[J].쓏뾪뺭볃퇐뺿,2004,5:79-84. [49]몫솼훇.Excel퓚춶샭닆훐뗄펦폃[M].놱뺩ꎺ뗧ퟓ릤튵돶냦짧,2005: 235-260. [50]킻뷰탇ꎬ톦틣. 폅뮯붨쒣폫LINDO\LINGO죭볾[M].놱뺩ꎺ쟥뮪듳톧돶냦짧,2005ꎺ98-134. [51]쳆킡컒ꎬ십폀뾪ꎬ퓸폂ꎬ퇮맰풪.쿖듺ퟩ뫏풤닢뫍ퟩ뫏춶뻶닟랽램벰펦폃[M].놱뺩ꎺ뿆톧돶냦짧,2003:156-247. [52]퓸폂ꎬ샮욽ꎬ췵횾룕ꎬ쇵늨.ퟩ뫏횤좯춶폫놾쫐뎡퇐뺿[M].놱뺩:뿆톧돶냦짧ꎬ2007:127-213. [53]뫲캪늨ꎬ탬돉쿍.횤좯ퟩ뫏춶뻶닟뗄β쒣탍[J].펦폃쫽톧,2000,3:25-30. [54]퓀캰ꎬ뫘탋쪱.쟸볤맦뮮퓚횤좯춶ퟩ뫏훐뗄펦폃[J].볛횵릤돌,2009, 9:63-66. 42
뢽슼 뢽 슼 뢽뇭A:퇹놾막욱52훜훜쫕엌볛뫍뾪엌볛 막욱쏻돆 췲 뿆ꏁ 훐맺욽낲 훐맺쪯폍 훐탋춨톶 헐짌틸탐 죕웚 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 2009-3-6 -3-13 -3-20 -3-27 -4-3 -4-9 -4-17 -4-24 -4-30 -5-8 -5-15 -5-22 -5-27 -6-5 -6-12 -6-19 -6-26 -7-3 -7-10 -7-17 -7-24 -7-31 -8-7 -8-14 -8-21 -8-28 -9-4 -9-11 -9-18 -9-25 -9-30 -10-9 -10-16 -10-23
믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍뫍쪵횤퇐뺿 2009-10-30 -11-6 -11-13 -11-20 -11-27 -12-4 -12-11 -12-18 -12-25 -12-31 -1-8 -1-15 -1-22 -1-29 -2-5 -2-12 -2-26 -3-5 막욱쏻돆 춭쇪폐즫 뺩뚫랽ꏁ 짏몣뗧솦 냼룖쾡췁 맺뗧쓏ퟔ 죕웚 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 2009-3-6 -3-13 -3-20 -3-27 -4-3 -4-9 -4-17 -4-24 -4-30 -5-8 -5-15 -5-22 -5-27 -6-5 -6-12 -6-19 -6-26 -7-3 -7-10 -7-17 -7-24 -7-31 -8-7
뢽슼 2009-8-14 -8-21 -8-28 -9-4 -9-11 -9-18 -9-25 -9-30 -10-9 -10-16 -10-23 -10-30 -11-6 -11-13 -11-20 -11-27 -12-4 -12-11 -12-18 -12-25 -12-31 -1-8 -1-15 -1-22 -1-29 -2-5 -2-12 -2-26 -3-5 막욱쏻돆 짏몣볒뮯 쯄뒨뎤뫧 냙듳벯췅 훐벯벯췅 탬릤믺킵 죕웚 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 2009-3-6 -3-13 -3-20 -3-27 -4-3 -4-9 -4-17 -4-24 -4-30 -5-8 -5-15 -5-22
믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍뫍쪵횤퇐뺿 2009-5-27 -6-5 -6-12 -6-19 -6-26 -7-3 -7-10 -7-17 -7-24 -7-31 -8-7 -8-14 -8-21 -8-28 -9-4 -9-11 -9-18 -9-25 -9-30 -10-9 -10-16 -10-23 -10-30 -11-6 -11-13 -11-20 -11-27 -12-4 -12-11 -12-18 -12-25 -12-31 -1-8 -1-15 -1-22 -1-29 -2-5 -2-12 -2-26 -3-5 막욱쏻돆 죊뫍튩튵 뗧맣뒫쎽 럡풭짺뮯 쓏 뺩 룛 좫 뻛 뗂 죕웚 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 뾪엌 쫕엌 2009-3-6
뢽슼 2009-3-13 -3-20 -3-27 -4-3 -4-9 -4-17 -4-24 -4-30 -5-8 -5-15 -5-22 -5-27 -6-5 -6-12 -6-19 -6-26 -7-3 -7-10 -7-17 -7-24 -7-31 -8-7 -8-14 -8-21 -8-28 -9-4 -9-11 -9-18 -9-25 -9-30 -10-9 -10-16 -10-23 -10-30 -11-6 -11-13 -11-20 -11-27 -12-4 -12-11 -12-18 -12-25 -12-31
믹폚쟸볤쫽뗄횤좯ퟩ뫏춶쒣탍뫍쪵횤퇐뺿 2010-1-8 -1-15 -1-22 -1-29 -2-5 -2-12 -2-26 -3-5 48
훂킻 훂 킻 퇛횮볤ꎬ죽쓪뗄퇐뺿짺톧쾰틑뷓뷼캲짹ꎬ퓚릥뛁쮶쪿톧캻웚볤뫍싛컄뗄킴ퟷ맽돌훐ꎬ컒뗃떽쇋뫜뛠샏쪦뫍춬톧뗄냯훺ꎬ횵듋싛컄돉룥횮볊ꎬ뷷쿲쯻쏇뇭쪾짮짮뗄뺴틢뫍훔탄뗄룐킻! 놾싛컄쫇퓚컒뗄떼쪦돂뮪폑뷌쫚뗄쾤탄횸떼뫍냯훺쿂췪돉뗄ꆣ죽쓪살ꎬ떼쪦풨늩뗄톧쪶ꆢ퇏뷷뗄훎톧뿆퇐첬뛈ꆢ컱쪵뗄릤ퟷퟷ럧ꆢ폫죋캪짆뗄뒦쫀럧룱룸쇋컒뫜듳뗄펰쿬늢붫쪹컒쫜틦훕짺ꎬ늢붫벤샸컒퓚틔뫳뗄죋짺뗀슷짏쟚쟚뿒뿒ꎬ첤첤쪵쪵ꆣ 떼쪦벴쪹짭퓚맺췢ꎬ떫뛔컒쏇뗄맘탄뫍뚽듙튲듓캴럅쯉맽ꆣ헽쫇떼쪦뗄퇔뒫짭뷌쪹컒퓚죽쓪톧쾰웚볤퓚캪죋ꆢ뒦쫀ꆢ톧쪶뗈룷랽쏦뗃떽좫쏦뫍뎤ퟣ뗄랢햹ꆣ퓚헢죽쓪뗄톧쾰짺믮훐폈웤쫇뷼웚싛컄킴ퟷ웚볤ꎬ컒짮짮뗘쳥믡떽떼쪦뛔컒쏇뗄맘낮ꎬ퓚듋쿲쯻뇭쪾짮짮뗄룐킻ꆣ 짮짮룐킻쪦탖훜샱룕샏쪦ꆢ췵쇁ꆢ믆죘뻪ꆢ쯯ꆢ태퓸뺲뗈춬톧퓚퇐뺿짺톧쾰웚볤ꎬ룸폨컒뗄냯훺ꎬ컒쯹좡뗃뗄쎿튻뗣돉벨뚼폫쯻쏇뗄맘탄뫍냯훺쫇럖늻뾪뗄ꎡ뮹튪룐킻컒뗄볒죋ꎬ쎻폐쯻쏇뛔컒톧튵짏뗄횧돖ꎬ컒늻쓜ퟟ떽뷱쳬ꆣ 쿲퓚놾죋릥뛁쮶쪿톧캻웚볤뗄릤짌맜샭톧풺뗄뛅열돌ꆢ컢돉쯌ꆢ훬퓆뻪ꆢ몫뚫쇖뷌쫚틔벰2007벶릤짌맜샭톧풺좫쳥퇐뺿짺뇭쪾컒훔탄뗄킻틢ꎡ ퟮ뫳ꎬ룐킻쯹폐짳퓄컒뗄싛컄뗄볒ꆢ듰뇧캯풱믡뗄좫쳥샏쪦틔벰?쇙듰뇧쿖뎡뗄룷캻샏쪦뫍춬톧ꆣ 쇵춤춤 2010쓪4퓂9죕 49
릥뛁쮶쪿톧캻웚볤뗄뿆퇐쟩뿶 릥뛁쮶쪿톧캻웚볤뗄뿆퇐쟩뿶 퇐뺿짺웚볤랢뇭싛컄ꎺ [1]쇵춤춤.컒맺뷰죚춶쳥쾵뗄럧쿕컊쳢퇐뺿[J].ퟜ닃ꎬ2009ꎬ9: 54-56. [2]쇵춤춤.횤좯춶ퟩ뫏샭싛뗄펦폃벰좱쿝컊쳢퇐뺿[J].쿖듺짌쎳릤튵ꎬ2009, 21: 139-141. 50
