An Asset-Liability Management model with a novel strategy for controlling risk of underfunding is presented in this paper. The basic model involves multiperiod 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 measure (and control) risk of underfunding. A small numerical example is provided to demonstrate advantages of this new model which includes stochastic dominance constraints over the basic model. Adding stochastic dominance constraints comes with a price. It complicates the structure of the underlying stochastic program. Indeed, new constraints create a link between variables associated with different scenarios of the same time stage. This destroys the usual treestructure of the constraint matrix in the stochastic program and prevents the application of standard stochastic programming approaches such as (nested) Benders decomposition. A structure-exploiting interior point method is applied to this problem. A specialized interior point solver OOPS can deal efficiently with such problems and outperforms the industrial strength commercial solver CPLEX. Computational results on medium scale problems with sizes reaching about one million of variables demonstrate the efficiency of the specialized solution technique. The solution time for these nontrivial asset liability models seems 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, and this makes the method applicable to truly large scale problems.

## Citation

Technical Report ERGO-09-002, School of Mathematics and Maxwell Institute for Mathematical Sciences University of Edinburgh January 15th, 2009

## Article

View Asset-Liability Management Modelling with Risk Control by Stochastic Dominance