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E-raamat: Risk Management for Pension Funds: A Continuous Time Approach with Applications in R

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This book presents a consistent and complete framework for studying the risk management of a pension fund. It gives the reader the opportunity to understand, replicate and widen the analysis. To this aim, the book provides all the tools for computing the optimal asset allocation in a dynamic framework where the financial horizon is stochastic (longevity risk) and the investor's wealth is not self-financed. This tutorial enables the reader to replicate all the results presented. The R codes are provided alongside the presentation of the theoretical framework. The book explains and discusses the problem of hedging longevity risk even in an incomplete market, though strong theoretical results about an incomplete framework are still lacking and the problem is still being discussed in most recent literature.

Arvustused

The book presents a consistent and complete framework for studying the risk management of a pension fund. It is useful for students and teachers in financial and actuarial mathematics as well as for professionals in the area of pension funds. (Pavel Stoynov, zbMATH 1460.91007, 2021)

1 Introduction
1(10)
1.1 The Structure of the Book
4(1)
1.2 The R Software
5(6)
References
8(3)
2 Decision Theory Under Uncertainty
11(26)
2.1 Introduction
11(1)
2.2 Decision Theory (Without Risk)
11(2)
2.3 Decision Theory (With Risk)
13(3)
2.4 Critics to the Expected Utility
16(2)
2.5 Risk Aversion
18(6)
2.6 The Stone-Geary Utility Function
24(1)
2.7 Certainty Equivalent on Financial Markets
25(4)
2.8 Utility and Time
29(2)
2.9 A First Pension Model
31(6)
References
36(1)
3 Stochastic Processes
37(20)
3.1 Introduction
37(1)
3.2 Deterministic Linear Differential Equation
37(1)
3.3 Stochastic Linear Differential Equation
38(3)
3.4 Stochastic Models Used in Finance
41(2)
3.5 Parameter Estimation
43(2)
3.6 The Interest Rate
45(6)
3.7 Simulation
51(2)
3.8 The State Variables
53(4)
References
55(2)
4 The Financial Market
57(26)
4.1 Introduction
57(1)
4.2 Financial Assets
57(1)
4.3 Portfolio and Wealth
58(3)
4.4 External Cash Flows and Modified Wealth
61(1)
4.5 Arbitrage
62(4)
4.6 Completeness (and Asset Pricing)
66(3)
4.7 Change of Probability and Asset Pricing
69(3)
4.8 Bond Pricing: Closed Form and Simulations
72(4)
4.9 The Switch Between Probabilities
76(3)
4.10 Change of Numeraire
79(1)
4.11 Assets with Coupons/Dividends
80(3)
References
82(1)
5 The Actuarial Framework
83(30)
5.1 Introduction
83(1)
5.2 Actuarial Measures
83(3)
5.3 Double Stochastic Force of Mortality and Asset Pricing
86(3)
5.4 Annuities in the Gompertz Framework
89(5)
5.5 The Human Mortality Database
94(2)
5.6 Estimation of the Gompertz Deterministic Model
96(4)
5.7 A Stochastic Model for the Force of Mortality
100(7)
5.8 A Stochastic Model for the Survival Probability
107(2)
5.9 The Evolution of Wealth Subject to Actuarial Risk
109(4)
References
111(2)
6 Financial-Actuarial Assets
113(10)
6.1 Introduction
113(1)
6.2 Derivatives on Human Life
113(3)
6.3 Longevity Bond
116(1)
6.4 The Tontine
117(2)
6.5 Death Bond
119(4)
Reference
122(1)
7 Pension Fund Management
123(46)
7.1 Introduction
123(1)
7.2 Contributions and Pensions
123(5)
7.3 Reserves
128(1)
7.4 Prospective Mathematical Reserve
129(4)
7.5 Fund's Budget Constraint
133(3)
7.6 Pension Fund's Ratios
136(1)
7.7 Fund's Optimisation Problem
137(1)
7.8 Dynamic Optimisation (the Martingale Approach)
138(6)
7.9 The Optimal Wealth
144(2)
7.10 The Speculative Portfolio Component
146(2)
7.11 The Speculative Portfolio Component: A Numerical Example
148(4)
7.12 Hedging Portfolio Component for Minimum Wealth
152(1)
7.13 Hedging Portfolio Component for Prospective Mathematical Reserve
153(1)
7.14 Hedging Portfolio Component for Discount Factor
154(4)
7.15 The Case of an Incomplete Market
158(2)
7.16 The Role of Longevity Bonds and Ordinary Bonds
160(4)
7.17 The Role of Longevity Bonds and Ordinary Bonds in an Incomplete Market
164(2)
7.18 The Inflation Risk
166(3)
Reference
168(1)
8 A Workable Framework
169(58)
8.1 Introduction
169(1)
8.2 The State Variables
169(3)
8.3 The Auxiliary Functions
172(6)
8.4 The Financial Market
178(2)
8.5 The Data
180(4)
8.6 Calibration of the Riskless Interest Rate
184(1)
8.7 Calibration of the ZCB
185(1)
8.8 Calibration of the Risky Asset
186(3)
8.9 Calibration of the Contributions
189(2)
8.10 The Behaviour of the Auxiliary Functions
191(10)
8.11 The Derivatives of the Auxiliary Functions
201(8)
8.12 The Simulations
209(7)
8.13 The Optimal Portfolio
216(11)
9 A Pure Accumulation Fund
227(12)
9.1 Introduction
227(1)
9.2 The Optimisation Problem
227(1)
9.3 The Optimal Portfolio
228(2)
9.4 A Workable Framework
230(2)
9.5 The Optimal Portfolio: Numerical Results
232(7)
Conclusions 239
Francesco Menoncin is Full Professor of Economic Policy at the University of Brescia, Italy. He has a Masters in Economics and a PhD in Economics both from Université Catholique de Louvain (Belgium), and a PhD in Economics from the University of Pavia (Italy). He teaches in the field of finance in Italy and France at Masters and PhDs. He has published articles and books about optimal control in financial market, asset prices, and risk management.
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