Stochastic Methods for Pension Funds.
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-know...
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| Other Authors: | , |
| Format: | eBook |
| Language: | English |
| Published: |
London :
Wiley,
2012.
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| Series: | ISTE.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Stochastic Methods for Pension Funds; Title Page; Copyright Page; Table of Contents; Preface; Chapter 1. Introduction: Pensions in Perspective; 1.1. Pension issues; 1.1.1. The challenge; 1.1.2. Some figures; 1.2. Pension scheme; 1.2.1. Definition; 1.2.2. The four dimensions of a pension scheme; 1.3. Pension and risks; 1.3.1. Demographic risks; 1.3.2. Financial risks; 1.3.3. Impact of the risks on various kinds of pension schemes; 1.3.4. The time horizon of a pension scheme; 1.4. The multi-pillar philosophy; Chapter 2. Classical Actuarial Theory of Pension Funding.
- 2.1. General equilibrium equation of a pension scheme2.1.1. Principles; 2.1.2. The retrospective reserve; 2.1.3. The prospective reserve; 2.1.4. Equilibrated pension funding; 2.1.5. Decomposition of the reserve; 2.1.6. Classification of the methods; 2.2. General principles of funding mechanisms for DB Schemes; 2.3. Particular funding methods; 2.3.1. Unit credit cost methods; 2.3.2. Level premium methods; 2.3.3. Aggregate cost methods; Chapter 3. Deterministic and Stochastic Optimal Control; 3.1. Introduction; 3.2. Deterministic optimal control.
- 3.2.1. Formulation of the optimal control problem3.3. Necessary conditions for optimality; 3.3.1. Bellman function; 3.3.2. Bellman optimality equation; 3.3.3. Hamilton-Jacobi equation; 3.3.4. The synthesis function; 3.3.5. Other types of optimal controls; 3.3.6. Example: the classical quadratic/linear control problem; 3.4. The maximum principle; 3.4.1. The maximum principle from the dynamic programming approach; 3.5. Extension to the one-dimensional stochastic optimal control; 3.5.1. Formulation of the one-dimensional stochastic optimal control problem.
- 3.5.2. Necessary conditions for one-dimensional stochastic optimality3.5.3. Extension to the multi-dimensional stochastic optimal control; 3.5.4. Dynamic programming principle; 3.5.5. The Hamilton-Jacobi-Bellman equation; 3.6. Examples; 3.6.1. Merton portfolio allocation problem; Chapter 4. Defined Contribution and Defined Benefit Pension Plans; 4.1. Introduction; 4.2. The defined benefit method; 4.3. The defined contribution method; 4.3.1. The model; 4.3.2. The capitalization system; 4.4. The notional defined contribution (NDC) method; 4.4.1. Historical preliminaries.
- 4.4.2. The Dini reform transformation coefficients4.4.3. Theoretical preliminaries; 4.4.4. The construction of a unitary pension present value; 4.4.5. Numerical example and results comparison; 4.5. Conclusions; Chapter 5. Fair and Market Values and Interest Rate Stochastic Models; 5.1. Fair value; 5.2. Market value of financial flows; 5.3. Yield curve; 5.4. Yield to maturity for a financial investment and for a bond; 5.5. Dynamic deterministic continuous time model for an instantaneous interest rate; 5.5.1. Instantaneous interest rate; 5.5.2. Particular cases.