‘Fund management’ discusses the objective to form portfolios of assets so as to maximize the investment return. A mathematical finance-oriented approach to optimal investment, in the context of the Black–Scholes price model, was proposed by Robert Merton in 1969. Fund management is a huge industry, and has become much more technical with the emergence of hedge funds deploying sophisticated strategies. There have been many attempts at constructing mathematical models for asset allocation that match real market behaviour more closely. The basic problem is that markets appear so erratic. Is there anything about them that is more invariant? The scenario tree model for long-term asset liability management is explained.