Stochastic programming approach to asset liability management under uncertainty

We have shown that the asset liability management under uncertainty can be modeled as stochastic programming problems. Specifically, we have explained that there are at least two different formulation approaches in modeling the asset liability management problems depending on how we view the future uncertainty.; We, then, proposed a new sampling method, called the event tree based sampling. The event tree based sampling procedure has been developed for multistage stochastic programming formulations with a binomial lattice movement as underlying uncertainty. Since the stochastic formulation of the asset liability management problem has a form of multistage stochastic programming and the uncertainty of the future is often described as a binomial lattice, the suggested sampling method is an appropriate sampling procedure for the asset liability management problem.; Finally, we developed a concept, called condition number. In particular we have studied the problem of conditioning of an optimal solution from the point of view of Monte Carlo sampling approximation approach. With the concept of condition number, we were able to characterize the well or ill conditioning of stochastic programming problems.