In this paper we develop a model of asset liability management for banking companies that maximises bank profits and minimises capital requirement in accordance with the Basel Accords. The model is based on fuzzy programming, which we use to solve a bi objective programme with crisp coefficients. Subsequently, we propose a fuzzy programming model that makes it possible to avoid the strict fulfilment of some constraints, i.e. they need only be complied with partially. In our opinion, the second approach is the most suitable of the two since constraints (related to strategic decisions, financial markets behaviour, etc.) are usually ill-defined.