Stochastic programming and stable distributions in asset-liability management

Michael J. Grebeck, Svetlozar T. Rachev and Frank J. Fabozzi

Abstract

ABSTRACT

Stochastic programming methods can be applied to portfolio optimization in the context of pension fund management. In this paper we apply stochastic programming wherein the allocations are found among various asset classes that optimize a trade-off between the risk and the expected final surplus wealth. A weighted average of the conditional value-at-risk of the surplus wealth over the time horizon is used as the multi-period measure of risk. Scenarios for the stochastic program are generated from two multivariate time series models that incorporate volatility clustering: the first assumes the innovations are normal and the second assumes the innovations are stable. Backtesting of the minimum risk portfolios is carried out to compare the performance of the single-stage problem with the two-stage recourse problem and the normal distribution with the stable distribution.