Titlebook: Mathematical Financial Economics; A Basic Introduction Igor V. Evstigneev,Thorsten Hens,Klaus Reiner Sche Textbook 2015 The Editor(s) (if a

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Portfolio Selection: Introductory CommentsThe chapter introduces fundamental notions related to asset prices, asset returns and investors’ portfolios. It describes the two-period model of an asset market, the basic framework for Part I of the book. It contains definitions of key mathematical notions used in the book.

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978-3-319-36249-6The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Mathematical Financial Economics978-3-319-16571-4Series ISSN 2192-4333 Series E-ISSN 2192-4341

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https://doi.org/10.1007/978-3-319-16571-4Arbitrage pricing; Capital growth theory; Evolutionary finance; Financial economics; Mathematical financ

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Properties of Efficient Portfoliosistics of these portfolios can be expressed. It is shown how to give a complete description in terms of A, B, C and D of the efficient frontier in the $?sigma$-$m$ plane and in the $?sigma?{2}$-$m$ plane. A key result is a two-fund theorem, which is formulated and proved. The chapter concludes with a geometric illustration of the two-fund theorem.

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The Markowitz Model with a Risk-Free Assetns, and describes the Markowitz optimization problem in this setting. A criterion for portfolio efficiency and an explicit formula for an efficient portfolio with the given risk tolerance are derived and discussed.

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