{"title":"马科维茨模型的另一种证明","authors":"Yaniv Zaks","doi":"10.2139/ssrn.2129137","DOIUrl":null,"url":null,"abstract":"In the fundamental paper on portfolio selection, Markowitz (1952) described via geometric reasoning his innovative theory and provided the explicit optimal selection for the cases of 3 and 4 assets. Merton (1972) obtained for the general case the efficient portfolio frontiers explicitly by using Lagrange multipliers. In this paper, we suggest a geometric approach to achieve the explicit optimal selection for the general case thus generalizing Markowitz’s original approach to achieve the explicit presentation of the desired selection.","PeriodicalId":174643,"journal":{"name":"Entrepreneurship Educator: Courses","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"An Alternative Proof to Markowitz's Model\",\"authors\":\"Yaniv Zaks\",\"doi\":\"10.2139/ssrn.2129137\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the fundamental paper on portfolio selection, Markowitz (1952) described via geometric reasoning his innovative theory and provided the explicit optimal selection for the cases of 3 and 4 assets. Merton (1972) obtained for the general case the efficient portfolio frontiers explicitly by using Lagrange multipliers. In this paper, we suggest a geometric approach to achieve the explicit optimal selection for the general case thus generalizing Markowitz’s original approach to achieve the explicit presentation of the desired selection.\",\"PeriodicalId\":174643,\"journal\":{\"name\":\"Entrepreneurship Educator: Courses\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Entrepreneurship Educator: Courses\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.2129137\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Entrepreneurship Educator: Courses","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.2129137","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In the fundamental paper on portfolio selection, Markowitz (1952) described via geometric reasoning his innovative theory and provided the explicit optimal selection for the cases of 3 and 4 assets. Merton (1972) obtained for the general case the efficient portfolio frontiers explicitly by using Lagrange multipliers. In this paper, we suggest a geometric approach to achieve the explicit optimal selection for the general case thus generalizing Markowitz’s original approach to achieve the explicit presentation of the desired selection.
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