DYNAMIC-STOCHASTIC PROGRAMMING FOR ASSET-LIABILITY MANAGEMENT

Multistage stochastic programming - in contrast to stochastic control - has found wide application in the formulation and solution of financ ial problems characterized by a large number of state variables and a generally low number of possible decision stages. The literature on th e use of multistage recourse modelling to formalize complex portfolio optimization problems dates back to the early seventies, when the tech nique was first adopted to solve a fixed income security portfolio pro blem. We present here the CALM model, which has been designed to deal with uncertainty affecting both assets (in either the portfolio or the market) and liabilities (in the form of scenario dependent payments o r borrowing costs). We consider as an instance a pension fund problem in which portfolio rebalancing is allowed over a long-term horizon at discrete time points and where liabilities refer to five different cla sses of pension contracts. The portfolio manager, given an initial wea lth, seeks the maximization of terminal wealth at the horizon, with in vestment returns modelled as discrete state random vectors. Decision v ectors represent possible investments in the market and holding or sel ling assets in the portfolio, as well as borrowing decisions from a cr edit line or deposits with a bank. Computational results are presented for a set of IO-stage portfolio problems using different solution met hods and libraries (OSL, CPLEX, OBI). The portfolio problem, with an u nderlying vector data process which allows up to 2688 realizations at the 10-year horizon, is solved on an IBM RS6000/590 for a set of twent y-four large-scale test problems using the simplex and barrier methods provided by CPLEX (the latter for either linear or quadratic objectiv e), the predictor/corrector interior point method provided in OBI, the simplex method of OSL, the MSLiP-OSL code instantiating nested Bender s decomposition with subproblem solution using OSL simplex, and the cu rrent version of MSLiP.