Application of stochastic programming and stable distributions to asset liability management

Multistage stochastic programming methods are applied to portfolio optimization in the context of asset liability management. These methods can incorporate rebalancing decisions and transaction costs to find optimal investment strategies over a time horizon. Additionally, assets and liabilities are considered in the same risk-reward optimization problem, thereby taking advantage of common risk factors.; The specific problem examined is that of a pension fund. The allocations are found among various asset classes that optimize a tradeoff between the risk and the expected final surplus wealth. A weighted average of the Conditional Value at Risk of the negative surplus wealth over the time horizon is used as the multiperiod measure of risk. This particular risk measure permits a formulation of the problem that has a convex, piecewise linear objective and linear constraints. A decomposition procedure in the solution method allows parallel implementation.; Uncertainty is represented through a scenario tree, resulting in a very large deterministic formulation of the stochastic program. The scenario generation procedures attempt to produce representative discrete distributions that will result in good decisions. The scenarios 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. Value at Risk backtesting of the time series models rejects the normality assumption and shows the superiority of the stable assumption.; Efficient frontiers for the 2-stage problem are found under both distributional assumptions. Backtesting of the minimum risk portfolios is carried out to compare the performance of the 1-stage problem with the 2-stage recourse problem and the normal distribution with the stable distribution. By computing the risk of the realized surplus wealths resulting from the optimal allocations, it is shown that the 2-stage recourse problem outperforms the 1-stage problem in dynamic backtesting with transaction costs. Portfolio backtesting in a static setting without transaction costs provides a better comparison of the distributional assumptions and shows that the stable assumption produces a smaller realized risk.