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.

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.

In this paper we propose and study a continuous time stochastic model of optimal allocation for a defined contribution pension fund with a minimum guarantee. Usually, portfolio selection models for pension funds maximize the expected utility from final wealth over a finite horizon (the retirement time), whereas our target is to maximize the expected utility from current wealth over an infinite horizon since we adopt the point of view of the fund manager.In our model the dynamics of wealth takes directly into account the flows of contributions and benefits and the level of wealth is constrained to stay above a solvency level. The fund manager can invest in a riskless asset and in a risky asset but borrowing and short selling are prohibited.We concentrate the analysis on the effect of the solvency constraint, analyzing in particular what happens when the fund wealth reaches the allowed minimum value represented by the solvency level.The model is naturally formulated as an optimal stochastic control problem and is treated by the dynamic programming approach. We show that the value function of the problem is a regular solution of the associated Hamilton-Jacobi-Bellman equation. Then we apply verification techniques to get the optimal allocation strategy in feedback form and to study its properties. We finally give a special example with explicit solution.

Countries around the world are increasingly relying on individual pension savings accounts to provide income in old age for their citizens. Although these funds have now been in place for several decades, their performance is usually measured using methods that are not meaningful in relation to this long-term objective. The recent global financial crisis has highlighted the need to develop better performance evaluation methods that are consistent with the retirement income objective of pension funds. Compiling research derived from a partnership among the World Bank, the Organisation for Economic Co-operation and Development (OECD), and three private partners, 'Evaluating the Financial Performance of Pension Funds' discusses the theoretical basis and key implementation issues related to the design of performance benchmarks based on life-cycle savings and investment principles. The book begins with an evaluation of the financial performance of funded pension systems using the standard mean variance framework. It then provides a discussion of the limitations inherent to applying these methods to pension funds and outlines the many other issues that should be addressed in developing more useful and meaningful performance measures through the formulation of pension-specific benchmark portfolios. Practical implementation issues are addressed through empirical examples of how such benchmarks could be developed. The book concludes with commentary and observations from several noted pension experts about the need for a new approach to performance measurement and the impact of the recent global financial crisis on pension funds.