Investment strategy is often static, punctuated by infrequent reviews. For most long-term investors, this practice results in large risks being taken that could otherwise be managed with a more dynamic investment policy. The bulk of this paper is aimed at analysing and describing two multi-period investment strategy problems — in order to derive potential dynamic strategies. Along the way, we show how static investment strategies can fail to deliver an investor's long-term objectives and describe the relationship of our work to other areas of the finance literature. This paper does not cover trading strategies such as Tactical Asset Allocation.

This paper sets out two main approaches to the multi-period problem. The first approach optimises a utility function. The second approach uses partial differential equation (PDE) technology to optimise a target statistic (in this case, TailVaR) subject to return and long-only constraints.

Acanthocephalans have evolved a hooked proboscis and some taxa have trunk spines to attach to their definitive hosts. These structures are generated before being used, thus a key question is how investment in attachment could optimally be allocated through the ontogeny. The number and arrangement of hooks and spines are never modified in the definitive host, but it is unclear whether these structures grow during adult development. A comparison of the size of trunk spines between cystacanths and adults of Corynosoma cetaceum and C. australe indicated that spines grow in both species, but only in females, which also had significantly larger spines than males. This sexual dimorphism did not result from pure allometry because the body of females was smaller, and did not grow more than that of males. However, having a longer lifespan, females would need to withstand the extreme flow conditions prevailing in marine mammals for longer, inducing different investment and development schedules for spines. Patterns of spine growth also differed between species: fore-trunk spines grew in both species, but hind-trunk spines did only in C. cetaceum. In conclusion, investment strategies on attachment may differ, not only between congeneric species of acanthocephalan, but also between sexes of the same species.

This paper shows how the powerful and flexible tool of stochastic modelling can be applied to a range of business decisions extending far beyond the asset allocation solutions that are common to many asset/liability modelling studies. The example used to demonstrate these techniques is a general insurance case study, but similar principles can be extended to many different business situations. At each stage of the analysis we consider the implications of modern financial theory on the management decision process together with a practical perspective on observed behaviour in the real world. Opportunities are taken to suggest directions in which further research may be of benefit to the actuarial profession.

Using the stochastic investment model proposed by Wilkie (1995) this paper simulates the progress of a specimen final salary pension scheme over a period of 25 years. Salary experience over the projection period is also assumed to be stochastic. The specimen scheme is assumed to be stable during the projection period with respect to age, pensionable salary in real terms and past pensionable service.

Regular deterministic valuations of the scheme are conducted during the projection period to determine the current level of funding of the scheme on both a discontinuance and an ongoing basis, and also to determine the future contribution rate required to meet the funding objective. The required contribution rate is calculated in accordance with the Inland Revenue surplus regulations and the Minimum Funding Requirement (MFR) introduced in the Pensions Act 1995.

The effect on the level of funding (and, hence, on the size of the required contribution rate) of using different investment strategies and of varying the pace of funding, by adopting both a traditional prudent valuation basis and a more realistic valuation basis, are also explored.