Actuarial management of closed defined benefit retirement schemes using stochastic simulations

Abstract

The provision of retirement payouts to employees through the use of defined benefits has been diminishing in popularity amongst employers for some time. One way in which this has been realised is through the closure of defined benefit schemes to new entrants, creating a subset of schemes that rapidly increase in maturity as the closed membership ages. The actuarial monitoring of these schemes is vitally important; due to their fixed time horizon the security of members' benefits is paramount. This thesis investigates the actuarial monitoring of closed defined benefit retirement schemes. This is done via a simulation approach of a model scheme, with economic and decrement factors varying stochastically. The desires of trustees and employer-sponsors are expressed numerically and the distribution of these desires analysed from the simulated output. In addition, a single objective function is developed, balancing the desires of all parties, in order to quantify the optimal use of investment and contribution strategies. In addition, adjustments to the model scheme are made to investigate their effect on the use of these strategies. It is found that schemes that are closed to new entrants should be invested more conservatively, but with surpluses and deficits allowed to be spread over a longer time frame than schemes that are open to new entrants. There is a strong trend towards a surplus of assets over liabilities, due to the lower boundary of a zero contribution rate when the scheme is in surplus but no corresponding upper boundary when the scheme is in deficit. This trend is exacerbated by the fact that there are no new liabilities entering the scheme through new entrants. Improvements in the minimum objective function can be obtained by spreading surplus only above a certain funding level, cash flow matching liabilities for pensions in payment, reducing investment risk as surplus grows and allowing for smoothing of asset levels in determining contribution rates.