Mathematical Financial Economics: A Basic Introduction
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham[u.a.]
Springer International Publishing
2015
|
| Series: | Springer Texts in Business and Economics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 224 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 3319165704 9783319165707 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Part I Mean-Variance Portfolio Analysis
1 Portfolio Selection: Introductory Comments........................ 3
1.1 Asset Prices and Returns..... —...........*................ 3
1.2 Investor’s Portfolio: Long and Short Positions ................ 4
1.3 Return on a Portfolio ......................................... 5
1.4 Mathematical Notation.......................................... 8
2 Mean-Variance Portfolio Analysis: The Markowitz Model............. 11
2.1 Basic Notions.............................................. i 1
2.2 Optimization Problem: Formulation and Discussion.............. 13
23 Assumptions................................................. 15
2.4 Efficient Portfolios and Efficient Frontier................... 16
3 Solution to lire Markowitz Optimization Problem................... 19
3.1 Statement of the Main Result.................................. 19
3.2 Discussion — *............................................. 21
33 Proof of the Main Result...................................... 23
4 Properties of Efficient Portfolios................................ 27
4.1 Mean and Variance of the Return on an Efficient Portfolio..... 27
4.2 Description of the Efficient Frontier......................... 29
4.3 A Fund Separation Theorem..................................... 30
5 The Markowitz Model with a Risk-Free Asset........................ 33
5.1 Data of the Model............................................. 33
5.2 Portfolio Optimization with a Risk-Free Asset................. 36
53 Solution to the Portfolio Selection Problem................... 38
6 Efficient Portfolios in a Market with a Risk-Free Asset........... 43
6.1 Expectations and Variances of Portfolio Returns............... 43
6.2 Efficient Frontier and the Capital Market Line................ 44
63 Tangency Portfolio............................................ 46
6.4 A Mutual Fund Theorem......................................... 50
vii
Contents
viii
7 Capita] Asset Pricing Model (CAPM)............................. 53
7.1 A General Result........................................... 53
7.2 An Equilibrium Approach to the CAPM........................ 55
7.3 The Shaipe-Lintner-MossmFormula............................ 59
8 CAPM Continued ................................................ 61
8.1 Security Market Line and the Pricing Formula............... 61
8.2 CAPM as a Factor Model..................................... 62
8.3 Applying Theory to Practice: Sharpe’s and Jensen’s Tests... 64
9 Factor Models and the Ross-Huberman APT........................ 69
9.1 Single- and Multi-Factor Models............................ 69
9.2 Exact Factor Pricing....................................... 71
9.3 Ross-Huberman APT: Model Description....................... 76
9.4 Formulation and Proof of the Main Result................... 78
10 Problems and Exercises I....................................... 83
Part II Derivative Securities Pricing
11 Dynamic Securities Market Model................................. 105
11.1 Multi-Period Model of an Asset Market....................... 105
11.2 Basic Securities and Derivative Securities.................. 108
11.3 No-Arbitrage Pricing: Mam Result.......................... 110
11.4 The No-Arbitrage Hypothesis and Net Present Value......... 112
12 Risk-Neutral Pricing.............................................. 115
12.1 Risk-Neutral Measures....................................... 115
12.2 Fundamental Theorem of Asset Pricing...................... 117
12.3 Asset Pricing in Complete Markets ........................ 119
13 The Cox-Ross—Rubinstein Binomial Model............................ 125
13.1 The Structure of the Model................................. 125
13.2 Completeness of the Model.......*.......................... 127
13.3 Constructing a Risk֊Neutral Measure.......*.........*..... 129
13.4 Examples ............................................... 132
14 American Derivative Securities .. ......................֊. ..... 137
14.1 The Notion of an American Derivative Security. ֊.......... 137
14.2 Risk֊Neutral Pricing of American Derivative Securities.... 139
14.3 The Pricing Algorithm ................................... 142
15 From Binomial Model to Black—Scholes Formula ., 145
15.1 Drift and Volatility...................................... 145
15.2 Modelling the Price Process............................... 146
15.3 Binomial Approximation of the Price Process............... 147
15.4 Derivation of the Black—Scholes Formula................... 150 16
16 Problems and Exercises II......................................... 157
Contents
IX
Part in Growth and Equilibrium
17 Capital Growth Theory............................................. 169
17.1 Growth-Optimal Investments.................................. 169
17.2 Strategies in Terms of Investment Proportions............... 171
17.3 Results for Simple Strategies............................... 173
18 Capital Growth Theory: Continued................................. 177
18.1 Log-Optimal Strategies...................................... 177
18.2 Growth-Optimal and Numeraire Strategies..................... 179
18.3 Growth-Optimality for General Strategies.................... 180
18.4 Volatility֊Induced Growth................................... 183
19 General Equilibrium Analysis of Financial Markets................ 187
19.1 Walrasian Equilibrium....................................... 187
19.2 On the Existence of Equilibrium............................. 190
19.3 Rational Expectations and Equilibrium Pricing............... 192
19.4 Arbitrage and Equilibrium............................. 194 20 21
20 Behavioral Equilibrium and Evolutionary Dynamics................. 197
20.1 A Behavioral Evolutionary Perspective....................... 197
20.2 Survival Strategies......................................... 201
20.3 Links to the Classical Theory............................... 203
21 Problems and Exercises III....................................... 205
Mathematical Appendices
A Facts from Linear Algebra.......................................... 215
B Convexity and Optimization....................................... 219
Sources
223
|
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| author | Evstigneev, Igor V. Hens, Thorsten 1961- Schenk-Hoppé, Klaus Reiner |
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| author_facet | Evstigneev, Igor V. Hens, Thorsten 1961- Schenk-Hoppé, Klaus Reiner |
| author_role | aut aut aut |
| author_sort | Evstigneev, Igor V. |
| author_variant | i v e iv ive t h th k r s h krs krsh |
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| dewey-ones | 330 - Economics |
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| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
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| physical | IX, 224 S. graph. Darst. 235 mm x 155 mm |
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| spelling | Evstigneev, Igor V. Verfasser (DE-588)170453359 aut Mathematical Financial Economics A Basic Introduction Igor Evstigneev ; Thorsten Hens ; Klaus Reiner Schenk-Hoppé Cham[u.a.] Springer International Publishing 2015 IX, 224 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer Texts in Business and Economics Finanzwissenschaft (DE-588)4121273-3 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Wirtschaft (DE-588)4066399-1 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Upper undergraduate Mathematical finance Financial economics Capital growth theory Evolutionary finance Portfolio analysis Arbitrage pricing Wirtschaftsmathematik (DE-588)4066472-7 s Finanzwissenschaft (DE-588)4121273-3 s Wirtschaft (DE-588)4066399-1 s DE-604 Finanzmathematik (DE-588)4017195-4 s 1\p DE-604 Hens, Thorsten 1961- Verfasser (DE-588)138727082 aut Schenk-Hoppé, Klaus Reiner Verfasser (DE-588)171648242 aut Erscheint auch als Online-Ausgabe 978-3-319-16571-4 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028015191&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Evstigneev, Igor V. Hens, Thorsten 1961- Schenk-Hoppé, Klaus Reiner Mathematical Financial Economics A Basic Introduction Finanzwissenschaft (DE-588)4121273-3 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Wirtschaft (DE-588)4066399-1 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4121273-3 (DE-588)4066472-7 (DE-588)4066399-1 (DE-588)4017195-4 |
| title | Mathematical Financial Economics A Basic Introduction |
| title_auth | Mathematical Financial Economics A Basic Introduction |
| title_exact_search | Mathematical Financial Economics A Basic Introduction |
| title_full | Mathematical Financial Economics A Basic Introduction Igor Evstigneev ; Thorsten Hens ; Klaus Reiner Schenk-Hoppé |
| title_fullStr | Mathematical Financial Economics A Basic Introduction Igor Evstigneev ; Thorsten Hens ; Klaus Reiner Schenk-Hoppé |
| title_full_unstemmed | Mathematical Financial Economics A Basic Introduction Igor Evstigneev ; Thorsten Hens ; Klaus Reiner Schenk-Hoppé |
| title_short | Mathematical Financial Economics |
| title_sort | mathematical financial economics a basic introduction |
| title_sub | A Basic Introduction |
| topic | Finanzwissenschaft (DE-588)4121273-3 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Wirtschaft (DE-588)4066399-1 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finanzwissenschaft Wirtschaftsmathematik Wirtschaft Finanzmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028015191&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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