Dynamic stochastic programmingfor asset-liability management

Abstract

Multistage stochastic programming - in contrast to stochastic control - has found wideapplication in the formulation and solution of financial problems characterized by a largenumber of state variables and a generally low number of possible decision stages. Theliterature on the use of multistage recourse modelling to formalize complex portfolio optimizationproblems dates back to the early seventies, when the technique was first adopted tosolve a fixed income security portfolio problem. We present here the CALM model, whichhas been designed to deal with uncertainty affecting both assets (in either the portfolio orthe market) and liabilities (in the form of scenario dependent payments or borrowing costs).We consider as an instance a pension fund problem in which portfolio rebalancing is allowedover a long-term horizon at discrete time points and where liabilities refer to five differentclasses of pension contracts. The portfolio manager, given an initial wealth, seeks the maximizationof terminal wealth at the horizon, with investment returns modelled as discretestate random vectors. Decision vectors represent possible investments in the market andholding or selling assets in the portfolio, as well as borrowing decisions from a credit lineor deposits with a bank. Computational results are presented for a set of 10-stage portfolioproblems using different solution methods and libraries (OSL, CPLEX, OB1). The portfolioproblem, with an underlying vector data process which allows up to 2688 realizations at the10-year horizon, is solved on an IBM RS6000y590 for a set of twenty-four large-scale testproblems using the simplex and barrier methods provided by CPLEX (the latter for eitherlinear or quadratic objective), the predictorycorrector interior point method provided in OB1,the simplex method of OSL, the MSLiP-OSL code instantiating nested Benders decompositionwith subproblem solution using OSL simplex, and the current version of MSLiP.