Liquidity management with fuzzy qualitative constraints

Abstract The treasurer of a bank must balance liquidity flows every day in an environment in which some future interest rates and transactions are known precisely, but some are uncertain. Decision support systems based on traditional mathematical programming approach find the optimal plan with respect to precise quantitative constraints provided by the user; we here suggest a procedure by which such systems can utilize probabilistic and Fuzzy qualitative constraints (e.g. “the treasury might have to cover a small deficit next Friday”). Each qualitative judgement is formalized by a discrete possibility distribution, which is converted to a discrete probability distribution; in this form the problem can be solved by the simple recourse method. Unexpected surpluses/deficits due to an uncertain future balance are evaluated in the objective function: by varying the evaluation coefficients along a scale from pessimistic to optimistic, we can obtain several solutions each adapted to a different risk policy.