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Abstract

This thesis is concerned with the funding of retirement benefits in a defined-benefit final salary pension plan. A simplified model is set up in order to investigate the evolution of the pension funding system in a random economic and demographic environment. The long-term objectives of benefit security, contribution stability and flexibility are highlighted and are shown to relate to the motivation for advance funding of benefits. Actuarial valuations are construed as control processes to achieve these objectives through the determination of a suitable funding policy. One aspect of the funding policy is the choice of a suitable contribution as economic and demographic experience unfolds and deviates from actuarial valuation assumptions. Efficient actuarial methods of liquidating such deviations are considered when general autoregressive rates of return are projected, when new entrants into the plan vary randomly, and when other stochastic perturbations, such as discretionary contributions, are included. Two particular methods of determining contributions are compared and one is found to be more efficient at achieving the long-term objectives of security and stability. Stochastic optimal contribution and asset allocation decisions over a finite term, under certain rigorous assumptions and in a two-asset model, are derived using the dynamic programming principle. The optimal contribution control resembles the proportional spreading of surpluses and deficits while the optimal asset allocation is found to be a portfolio that dynamically hedges against the risk of inadequate benefit provision and unstable contributions. The methodology of actuarial valuations is examined qualitatively and the concept of a hedging or matching portfolio is found to be central to the valuation of pension plans, whether a market-oriented or a cash flow-oriented method is adopted. Various pension fund asset valuation methods are contrasted. The mathematical symmetry between asset gain/loss amortization and asset valuation is emphasised and an efficient way of determining actuarial asset values is investigated. Finally, the concept of economic prudence in actuarial valuations is explored in terms of the margins allowed in the choice of the discount rate (net of salary inflation) employed to value liabilities. The reasons for such prudence and its implications on funding are considered. It is well-known that conservatism leads to surpluses. Excessive and volatile surpluses as well as variable sponsor contributions must be avoided while retaining prudent funding objectives. A few simple methods (including an original method) to achieve this are studied. Some suggestions for further work are also discussed.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HJ Public Finance
Departments:	Bayes Business School > Actuarial Science & Insurance Bayes Business School > Bayes Business School Doctoral Theses Doctoral Theses

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