Risk management and decision making in defined benefit pension schemes
stochastic approach to decision-making in defined benefit pension schemes is presented. Existing decision-making tools in the form of actuarial valuations and asset and liability modelling are discussed. These tools are shown to be inadequate to fully address the objectives of the various stakeholders. Pension fund control using a quadratic criteria with linear factors is studied in the case where the fund is invested in a risk-free asset and a risky asset. Optimal asset allocation strategies are shown to be counter-intuitive. The optimal strategy is shown to involve increasing the allocation in the risky asset as the fund deficit increases and increasing the allocation in the risk-free asset as the fund deficit decreases. It is further shown that increasing the weight on the linear factors leads to an increase in the optimal allocation in the risky asset. A risk management approach to decision-making is presented. This is shown to be a more satisfactory decision-making tool in terms of setting the funding and investment strategies. The objectives of the stakeholders are addressed through downside risk measures and a performance measure for the cost. Methods of solving the problem are discussed: an indifference curve approach and a stochastic multi-objective approach leading to Pareto optimal solutions. It is shown that, in the indifference curve approach, an "efficient region" exists. This efficient region is such that all funding and investment strategies outside this region are inefficient; that is, such strategies can be improved by choosing strategies in the region. On the other hand in the multi-objective approach, pareto optimal investment strategies are located along an "efficient frontier". An extension to the stochastic approach is presented. Optimal funding and asset allocation strategies, over a range of projection horizons, are determined by taking into account the probability of default by the sponsoring employer. It is shown that, over a short-term horizon, bond-only asset allocation strategies are optimal, whilst over a longer horizon equity-backed asset allocation strategies are optimal.