Stochastic Methods for Pension Funds (eBook)

Pierre Devolder, Jacques Janssen, Raimondo Manca (Autoren)

eBook Download: PDF | EPUB

2013 | 1. Auflage
320 Seiten
John Wiley & Sons (Verlag)
978-1-118-56593-3 (ISBN)

Infos

Quantitative finance has become these last years a extraordinary
field of research and interest as well from an academic point of
view as for practical applications.

At the same time, pension issue is clearly a major economical
and financial topic for the next decades in the context of the
well-known longevity risk. Surprisingly few books are devoted to
application of modern stochastic calculus to pension analysis.

The aim of this book is to fill this gap and to show how recent
methods of stochastic finance can be useful for to the risk
management of pension funds. Methods of optimal control will be
especially developed and applied to fundamental problems such as
the optimal asset allocation of the fund or the cost spreading of a
pension scheme. In these various problems, financial as well
as demographic risks will be addressed and modelled.

Autor

Pierre De Volder, Full-time Professor, UCL; President of the Institut des Sciences Actuarielles, UCL; Member of The Royal Association of Belgian Actuaries (ARAB / KVBA). Jacques Janssen, Universite Libre de Bruxelles. Raimondo Manca, Università degli Studi di Roma La Sapienza.

Inhalt

Preface xiii

Chapter 1. Introduction: Pensions in Perspective 1

1.1. Pension issues 1

1.2. Pension scheme 7

1.3. Pension and risks 11

1.4. The multi-pillar philosophy 14

Chapter 2. Classical Actuarial Theory of Pension Funding
15

2.1. General equilibrium equation of a pension scheme 15

2.2. General principles of funding mechanisms for DB Schemes
21

2.3. Particular funding methods 22

Chapter 3. Deterministic and Stochastic Optimal Control
31

3.1. Introduction 31

3.2. Deterministic optimal control 31

3.3. Necessary conditions for optimality 33

3.4. The maximum principle 42

3.5. Extension to the one-dimensional stochastic optimal control
45

3.6. Examples 52

Chapter 4. Defined Contribution and Defined Benefit Pension
Plans 55

4.1. Introduction 55

4.2. The defined benefit method 56

4.3. The defined contribution method 57

4.4. The notional defined contribution (NDC) method 58

4.5. Conclusions 93

Chapter 5. Fair and Market Values and Interest Rate
Stochastic Models 95

5.1. Fair value 95

5.2. Market value of financial flows 96

5.3. Yield curve 97

5.4. Yield to maturity for a financial investment and for a bond
99

5.5. Dynamic deterministic continuous time model for an
instantaneous interest rate 100

5.6. Stochastic continuous time dynamic model for an
instantaneous interest rate 104

5.7. Zero-coupon pricing under the assumption of no arbitrage
114

5.8. Market evaluation of financial flows 130

5.9. Stochastic continuous time dynamic model for asset values
132

5.10. VaR of one asset 136

Chapter 6. Risk Modeling and Solvency for Pension Funds
149

6.1. Introduction 149

6.2. Risks in defined contribution 149

6.3. Solvency modeling for a DC pension scheme 150

6.4. Risks in defined benefit 170

6.5. Solvency modeling for a DB pension scheme 171

Chapter 7. Optimal Control of a Defined Benefit Pension
Scheme 181

7.1. Introduction 181

7.2. A first discrete time approach: stochastic amortization
strategy 181

7.3. Optimal control of a pension fund in continuous time
194

Chapter 8. Optimal Control of a Defined Contribution Pension
Scheme 207

8.1. Introduction 207

8.2. Stochastic optimal control of annuity contracts 208

8.3. Stochastic optimal control of DC schemes with guarantees
and under stochastic interest rates 223

Chapter 9. Simulation Models 231

9.1. Introduction231

9.2. The direct method 233

9.3. The Monte Carlo models 250

9.4. Salary lines construction 252

Chapter 10. Discrete Time Semi-Markov Processes (SMP) and
Reward SMP 277

10.1. Discrete time semi-Markov processes 277

10.2. DTSMP numerical solutions 280

10.3. Solution of DTHSMP and DTNHSMP in the transient case: a
transportation example 284

10.4. Discrete time reward processes 294

10.5. General algorithms for DTSMRWP 304

Chapter 11. Generalized Semi-Markov Non-homogeneous Models
for Pension Funds and Manpower Management 307

11.1. Application to pension funds evolution 307

11.2. Generalized non-homogeneous semi-Markov model for manpower
management 338

11.3. Algorithms 347

APPENDICES 359

Appendix 1. Basic Probabilistic Tools for Stochastic Modeling
361

Appendix 2. Itô Calculus and Diffusion Processes 397

Bibliography 437

Index 449

Produkt-Details

• Erscheint lt. Verlag: 4.3.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Recht / Steuern ► Wirtschaftsrecht
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Finanzierung
• Schlagworte: Altersversorgung • Angewandte Mathematik • Applied mathematics • Finanz- u. Wirtschaftsstatistik • Institutionelle Finanzplanung • Mathematics • Mathematik • Statistics • Statistics for Finance, Business & Economics • Statistik
• ISBN-10: 1-118-56593-2 / 1118565932
• ISBN-13: 978-1-118-56593-3 / 9781118565933