An Asset Liability Management model with a novel strategy for controlling the risk of underfunding is presented in this article. The basic model involves multi-period decisions (portfolio rebalancing) and deals with the usual uncertainty of investment returns and future liabilities. Therefore, it is well suited to a stochastic programming approach. A stochastic dominance concept is applied to control the risk of underfunding through modelling a chance constraint. A small numerical example and an out-of-sample backtest are provided to demonstrate the advantages of this new model, which includes stochastic dominance constraints, over the basic model and a passive investment strategy. Adding stochastic dominance constraints comes with a price. This complicates the structure of the underlying stochastic program. Indeed, the new constraints create a link between variables associated with different scenarios of the same time stage. This destroys the usual tree structure of the constraint matrix in the stochastic program and prevents the application of standard stochastic programming approaches, such as (nested) Benders decomposition and progressive hedging. Instead, we apply a structure-exploiting interior point method to this problem. The specialized interior point solver, object-oriented parallel solver, can deal efficiently with such problems and outperforms the industrial strength commercial solver CPLEX on our test problem set. Computational results on medium-scale problems with sizes reaching about one million variables demonstrate the efficiency of the specialized solution technique. The solution time for these non-trivial asset liability models appears to grow sublinearly with the key parameters of the model, such as the number of assets and the number of realizations of the benchmark portfolio, which makes the method applicable to truly large-scale problems.