 | Hillebrand M. Pension systems, demographic change, and the stock market. - Berlin; Heidelberg: Springer, 2008. - viii, 176 p. - (Lecture notes in economics and mathematical systems; 610). - Ref.: p.173-176. - ISBN 978-3-540-77972-8; ISSN 0075-8442
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1. Introduction ................................................. 1
Part I The Model
2. The General Model ........................................... 11
2.1. Overlapping Generations of Consumers ................... 11
2.2. Decision Problem of Consumers .......................... 13
2.3. Consumer Demand ........................................ 20
2.4. Decision Problem of Firms .............................. 29
2.5. Temporary Equilibrium .................................. 37
2.6. Pension Systems and Demographic Change ................. 42
2.A. Mathematical Appendix .................................. 45
2.A.1. Proof of Lemma 2.2.2 ............................ 45
2.A.2. Proof of Lemma 2.3.1 ............................ 46
2.A.3. Proof of Theorem 2.1 ............................ 47
2.B. Technical Lemmas ....................................... 51
3. The Parameterized Model ..................................... 55
3.1. Consumer Demand with Logarithmic Utility ............... 56
3.2. Asset Demand with Elliptical Distributions ............. 60
3.3. Demand Behavior of Firms ............................... 69
3.4. Temporary Equilibrium and Expectations Formation ....... 72
3.5. The Model in Period t .................................. 80
3.A. Mathematical Appendix .................................. 83
3.A.1. Proof of Lemma 3.1.1 ............................ 83
3.A.2. Proof of Proposition 3.1.1 ...................... 85
3.A.3. Properties of Elliptical Distributions .......... 86
3.A.4. Proof of Proposition 3.2.1 ...................... 90
3.A.5. Proof of Lemma 3.2.1 ............................ 91
3.A.6. Proof of Lemma 3.4.1 ............................ 93
3.B. Technical Lemmas ....................................... 97
Part II The Simulation Study
4. Pension Systems in the Presence of a Stationary
Population ................................................. 101
4.1. Dynamics of the Model ................................. 102
4.2. The Simulation Model .................................. 105
4.3. Impact of Pension Systems on Real and Financial
Markets ............................................... 116
4.4. Impact of Pension Systems on Consumer Welfare ......... 124
4.5. Robustness of Results ................................. 130
4.6. Reducing the Public Pension System .................... 135
4.A. Mathematical Appendix ................................. 141
4.A.1. Concepts from Random Dynamical Systems
Theory ......................................... 141
4.A.2. Proof of Lemma 4.4.1 ........................... 143
5. Pension Systems in the Presence of Demographic
Change ..................................................... 145
5.1. Population Dynamics and Demographic Change ............ 146
5.2. Constant Contributions ................................ 149
5.3. Reducing Contributions ................................ 153
5.4. Increasing Contributions .............................. 159
5.5. Increasing the Retirement Age ......................... 163
6. Conclusions and Outlook .................................... 169
References .................................................... 173
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