This paper presents and empirically evaluates two approaches to accounting for forecast uncertainty when attempting to optimize the operation of a residential battery energy storage system. Data-driven methods are used for forecasting, and dynamic programming, within a receding horizon controller, is used for operational optimization. The first method applies a discount factor to costs incurred at later intervals in a deterministic dynamic programming control horizon, provided with point forecasts. In the second approach probabilistic (scenario) forecasts are generated using Lloyd-Max quantization of the distribution of forecast errors, to allow the use of a stochastic dynamic programming formulation. These methods are applied to maximizing the cost-savings delivered from a residentially owned and operated battery, using a case-study of residential consumers with roof-top PV systems in New South Wales, Australia. It is found that scenario forecasts can offer an 8% increase in annual cost-savings, on average, when using a univariate multiple linear regression forecast.