Stabilizing Implementable Decisions in Dynamic Stochastic Programming
29 Pages Posted: 8 Jan 2015
Date Written: January 6, 2015
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. Conventional approaches to such problems have been 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 form 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. 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.
Keywords: discretization bias, stability, implementable decisions, sampling errror, dynamic stochastic programming
JEL Classification: C61, G11, G17
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