A Dynamic Model for Pension Funds Management.pdf

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A DYNAMIC MODEL FOR PENSION FUNDS MANAGEMENT 361 A DYNAMIC MODEL FOR PENSION FUNDS MANAGEMENT JEAN-FRAKCOIS BOULIER DIRECTHJRD~LAFCECHERCHEETDEL'INNOVA?‘ION ETIENNE TRUSSANT INGENIEURFINANCIBR CCF,103 AVEN~D~SCIIAMI'SELYS~~S 75008 PARIS DANIELE FLORENS PROFL~SEUR UNIVERW~DEPARIS IX DAUPMINE TEL. : 33 140 70 32 76 FAX : 33 140 70 30 31 ABSTRACT The management of pension funds financial encompasses asset allocation and the control of the future flows of contributions. A high proportion of stocks in the portfolio has the benefit of a lower mean contribution level, but at the price of a higher time variation of contribution flows. This paper models the trade-off in a inter-temporal framework and uses of stochastic control to obtain an optimal asset allocation -between a risky asset and a riskless asset- and the contribution policy. The solution in the case of a defined benefit scheme shows that the proportion of the risky asset and the level of contribution are both proportional to the difference between the maximum wealth necessary to fund all pensions, and the actual wealth of the pension fund. Illustrative simulations for France, US and Japan for various periods show a decrease of the contribution level down to zero after some decades. The hypothesis made and some shortcomings of the model are discussed and further research is outlined.
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A DYNAMIC MODEL FOR PENSION FUNDS MANAGEMENT 363 I Tntrocluction The economic role of pension funds is considerable and well acknowledged even in countries where the pay-as-you-go systemis dominant. Indeed, at their mature stage, which they are at in many Anglo-Saxon countries, pension fund assets represent a large percentage of stock and bond market capitalisation, in size comparable with the country’s GNP, and the contribution flows to the pension fund account for a significant part of personal savings. Moreover, their final objective -to pay pensions to workers in their old age- is of up- most importance for the social and political stability of the wealthy economies. How to manage pension provisions adequately is thus a crucial question. The principles underlying pension funds are quite simple, even if the variety of actual schemes from one country or one industry to another is vast and complex. Workers and corporations pay contributions to a pension fund, which invests them over a very long period of time and releases them when the workers retire, in the form of pensions. Obviously, the more the contribution, the higher should be the pension. Nevertheless, asset allocation also comes into play, in so far as that even a slight improvement of the asset portfolio mean return, say one or two percent, may result after thirty years of accumulation, in a sizeable increase -by 40% to lOO%- of the pensions. On the other hand, too much exposure to stock market fluctuations could, in the absence of careful management of the asset portfolio, severely damage the asset value and impose an undesirable increase of the contributions.
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