8. Stabilizing Implementable Decisions in Dynamic Stochastic Programming

We present a novel approach to address sampling error when discretely approximating a dynamic stochastic programme with a limited finite number of scenarios to represent the underlying path probability distribution. This represents a tentative solution to the problems first identified in our companion paper (Dempster et al., A comparative study of sampling methods for stochastic programming, forthcoming). Conventional approaches to such problems have been to find the best discretization of the statistical properties of the simulated processes in terms of the objective of the problem based on probability metrics. Here we consider the stability of the implementable decisions of a stochastic programme, which is key to financial investment and asset liability management (ALM) problems, while simultaneously reducing the discretization bias resulting from small-sample scenario discretization. We tackle discretization error by reducing the degrees of freedom of the decision space in a financially meaningful way by constraining the decisions to lie within a carefully chosen subspace. This avoids overfitting the optimized decisions to the simulated in-sample scenarios which often do not generalize to unseen scenarios drawn from the same probability distribution of paths. We illustrate the application of versions of the proposed technique using a practical four-stage ALM problem previously studied in Dempster et al. (J Portf Manag 32(2):51–61, 2006. Empirical results show their effectiveness in reducing the discretization bias and improving the stability of the implementable decisions without adding much to the computational complexity of the original problem.