Risk Management for Pension Funds: A Continuous Time Approach with Applications in R (EURO Advanced Tutorials on Operational Research)

Contents
1 Introduction
	1.1 The Structure of the Book
	1.2 The R Software
	References
2 Decision Theory Under Uncertainty
	2.1 Introduction
	2.2 Decision Theory (Without Risk)
	2.3 Decision Theory (With Risk)
	2.4 Critics to the Expected Utility
	2.5 Risk Aversion
	2.6 The Stone–Geary Utility Function
	2.7 Certainty Equivalent on Financial Markets
	2.8 Utility and Time
	2.9 A First Pension Model
	References
3 Stochastic Processes
	3.1 Introduction
	3.2 Deterministic Linear Differential Equation
	3.3 Stochastic Linear Differential Equation
	3.4 Stochastic Models Used in Finance
	3.5 Parameter Estimation
	3.6 The Interest Rate
	3.7 Simulation
	3.8 The State Variables
	References
4 The Financial Market
	4.1 Introduction
	4.2 Financial Assets
	4.3 Portfolio and Wealth
	4.4 External Cash Flows and Modified Wealth
	4.5 Arbitrage
	4.6 Completeness (and Asset Pricing)
	4.7 Change of Probability and Asset Pricing
	4.8 Bond Pricing: Closed Form and Simulations
	4.9 The Switch Between Probabilities
	4.10 Change of Numéraire
	4.11 Assets with Coupons/Dividends
	References
5 The Actuarial Framework
	5.1 Introduction
	5.2 Actuarial Measures
	5.3 Double Stochastic Force of Mortality and Asset Pricing
	5.4 Annuities in the Gompertz Framework
	5.5 The Human Mortality Database
	5.6 Estimation of the Gompertz Deterministic Model
	5.7 A Stochastic Model for the Force of Mortality
	5.8 A Stochastic Model for the Survival Probability
	5.9 The Evolution of Wealth Subject to Actuarial Risk
	References
6 Financial-Actuarial Assets
	6.1 Introduction
	6.2 Derivatives on Human Life
	6.3 Longevity Bond
	6.4 The Tontine
	6.5 Death Bond
	Reference
7 Pension Fund Management
	7.1 Introduction
	7.2 Contributions and Pensions
	7.3 Reserves
	7.4 Prospective Mathematical Reserve
	7.5 Fund's Budget Constraint
	7.6 Pension Fund's Ratios
	7.7 Fund's Optimisation Problem
	7.8 Dynamic Optimisation (the Martingale Approach)
	7.9 The Optimal Wealth
	7.10 The Speculative Portfolio Component
	7.11 The Speculative Portfolio Component: A Numerical Example
	7.12 Hedging Portfolio Component for Minimum Wealth
	7.13 Hedging Portfolio Component for Prospective Mathematical Reserve
	7.14 Hedging Portfolio Component for Discount Factor
	7.15 The Case of an Incomplete Market
	7.16 The Role of Longevity Bonds and Ordinary Bonds
	7.17 The Role of Longevity Bonds and Ordinary Bonds in an Incomplete Market
	7.18 The Inflation Risk
	Reference
8 A Workable Framework
	8.1 Introduction
	8.2 The State Variables
	8.3 The Auxiliary Functions
	8.4 The Financial Market
	8.5 The Data
	8.6 Calibration of the Riskless Interest Rate
	8.7 Calibration of the ZCB
	8.8 Calibration of the Risky Asset
	8.9 Calibration of the Contributions
	8.10 The Behaviour of the Auxiliary Functions
	8.11 The Derivatives of the Auxiliary Functions
	8.12 The Simulations
	8.13 The Optimal Portfolio
9 A Pure Accumulation Fund
	9.1 Introduction
	9.2 The Optimisation Problem
	9.3 The Optimal Portfolio
	9.4 A Workable Framework
	9.5 The Optimal Portfolio: Numerical Results
Conclusions