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Longevity risk is a major issue for insurers and pension funds, especially in the selling of annuity products. In that respect, securitization of this risk could offer great opportunities for hedging. This article proposes to design survivor bonds which could be issued directly by insurers. In order to guaranty some transparency in the product, the survivor bond is based on a public mortality index. The classical Lee-Carter model for mortality forecasting is used to price a risky coupon survivor bond based on this index.

The aim of this presentation is to motivate the pension adequacy issue in unfunded DC pension schemes (NDCs); develop a pricing framework for guarantees in unfunded pension systems; and compare it to the insurance and nancial markets framework.

The notional defined contribution pension scheme combines pay-as-you-go fi- nancing and a defined contribution pension formula. The return on contributions is based on a notional rate which is linked to an external index set by law, such as the growth rate of GDP, average wages, or contribution payments. The volatility of this return may introduce a pension adequacy problem in the system and therefore guarantees may be needed. Here we focus on the guarantee of a minimum return on the contributions made to the pension scheme and we calculate its price in a utility indifference framework. We obtain a closed-form solution in a general dependence structure with exponential preferences and in presence of stochastic short interest rates.

This paper addresses some of the problems a majority of retired individuals face: Why and in what proportion should they invest in a life annuity to maximize the utility of their future consumption or a bequest? The market considered in this work is made up of three assets: a life annuity, a risky asset and a cash account. As this problem doesn’t accept any suitable explicit solution, it is numerically solved by the Markov Chain approximation developed by Kushner and Dupuis. Without a bequest motive, we observe that the optimal planning of consumption is divided into two periods and that optimal asset allocation should include the risky asset. Next, the influence of a bequest on consumption and investment pattern is developed. We demonstrate that even with a bequest motive, pensioners should allocate a part of their wealth to the purchase of life annuities.

Investment guarantees are amongst the most important topics in the pricing and management of life insurance. Traditionally, two ways of analyzing the risk are possible: on the one hand, the financial approach based on risk-neutral measure and leading to option pricing and continuous hedging strategy and on the other hand, a more actuarial approach based on ruin probability and distribution of surplus. The purpose of this paper is to try to integrate these two approaches in the management of life insurance contracts with profits. First, we analyze in terms of value at risk and conditional value at risk the effect of putting an investment guarantee. This will be done in an ALM framework, based on different investment strategies of the insurer in terms of risk and matching between assets and liabilities. The liability side will be represented by a guaranteed technical rate; the asset side will be a mix of stocks, cash and bonds in a Gaussian environment with different matching strategies. Consequences of an investment choice in terms of ruin probability and level of solvency will be illustrated. In a second step, fair valuation principles are used in order to compute the market value of the contract and fix the participation rate of the contract.

The purpose of this paper is to show how stochastic optimal control theory can be applied to find an optimal investment policy before and after retirement in a defined contribution pension plan where benefits are paid under the form of annuities; annuities are supposed to be guaranteed during a certain fixed period of time. Using different kinds of utility functions we try to look at different strategies on the one hand in the investment part (i.e. before retirement) and on the other hand in the payment part (i.e. after retirement). The needed change of strategy after retirement can be interpreted in this model as a typical ALM constraint taking into account a guaranteed technical interest rate used by the insurer.

Defined Benefit Pension Schemes (DB) are affected by a lot of different risks able to put in danger the viability of the system. A solvency analysis seems therefore to be essential as in insurance but it must take into account the specificities of pension liabilities. In particular, pension funds are characterized by a long term aspect and a limited need of liquidity. In this perspective, the purpose of this paper is to combine the three major risks affecting a DB plan (market, inflation and longevity risks) and to look at their effect on the solvency of the pension fund.

We provide a self-contained analysis of a class of continuous-time stochastic mortality models that have gained popularity in the last few years. We describe some of their advantages and limitations, examining whether their features survive equivalent changes of measures. This is important when using the same model for both market-consistent valuation and risk management of life insurance liabilities. We provide a numerical example based on the calibration to the French annuity market of a risk-neutral version of the model proposed by Lee and Carter (1992).

The management of a life insurance portfolio or pension fund must take intoaccount the temporal evolution of its liabilities and its assets through some variables:the factors and returns. Their behaviour is analysed statistically and we deduce it to avector error correction model (VECM). Using the VECM obtained and by means ofsimulations different trajectories are generated, for each factors and returns, or scenarioswith an associated probability of occurrence. The risk measures, that we propose,analyse the assets and liabilities risk generated together in a dynamic and multiperiodicalprocess, and it is the main contribution of this paper. La gestión de carteras de vida de las compañías de seguros o de un fondo de pensiones debe tener en cuenta la evolución temporal de sus obligaciones y activos, a través del análisis de una serie de variables: factores y rendimientos. El comportamiento de estos es analizado, en este trabajo, estadísticamente y se modeliza mediante un vector de corrección de errores (VECM). A través de simulaciones, aplicando el VECM, se generan diferentes trayectorias, de cada una de los factores y rendimientos, las cuales denominamos escenarios con una probabilidad de ocurrencia asociada. Las medidas de riesgo que se proponen analizan el riesgo de activos y pasivos de forma conjunta, dinámica y multiperiódica, siendo todo ello la principal aportación del trabajo.

International audience; This chapter deals with the French PAYGO mandatory occupational pension scheme for the private sector workers (AGIRC-ARRCO), one of the world’s oldest pension point systems. In a first section, we trace the history of the setup of this system which relies on a particular mode of governance (joint administration by trade union and employers’ respective representatives). The second section is dedicated to the analysis of the tax distortion properties of the calculation rule of this defined contribution supplementary pension system. We also discuss the similarities with the German and Swedish pension systems. Weakened by the 2008 economic crisis, this jointly administered French supplementary pension scheme had to undergo a severe adjustment in “emergency mode” (Turner, Social security financing: Automatic adjustments to restore solvency, Washington, DC: AARP Public Policy Institute, 2009), in October 2015. We detail this agreement and show how it restores medium term balance and enacts the principles of sustainable governance.

International audience; Maintaining retirement systems stability is nowadays a big challenge for all countries. Such sustainability is widely related to a set of time-varying elements that include population structure, longevity, employment, and affiliation to social security. For the case of Algeria, public retirement works according to the pay-as-you-go principle and equilibrium is maintained by public subsidy. But, population is now aging, and longevity is improving. The retired population is supposed to grow faster than the population at working age. Consequently, it will be harder to keep equality between retirement incomes and outcomes especially if we consider the weakness of the demand for social security among workers. The latter remains widely dependent on public employment; the employees of the private sector are less covered. In the present paper, we aim to simulate the future evolution of the demographic and economic factors affecting the stability of the Algerian retirement system in order to show their long-run effect. As a result, we found that it will be impossible to keep the retirement sustainability within its current design. The accelerating aging process imposes to undertake heavy reforms in the near future.