Large-scale financial planning via a partially observable stochastic dual dynamic programming framework

Abstract

The multi-stage stochastic programming (MSP) approach is widely used to solve financial planning problems owing to its flexibility. However, the size of an MSP problem grows exponentially with the number of stages, and such problem can easily become computationally intractable. Financial planning problems often consider planning horizons of several decades, and thus, the curse of dimensionality can become a critical issue. Stochastic dual dynamic programming (SDDP), a sampling-based decomposition algorithm, has emerged to resolve this issue. While SDDP has been successfully implemented in the energy domain, few applications of SDDP are found in the finance domain. In this study, we identify the major obstacle in using SDDP to solve financial planning problems to be the stagewise independence assumption and propose a partially observable SDDP (PO-SDDP) framework to overcome such limitations. We argue that the PO-SDDP framework, which models uncertainties using discrete-valued partially observable Markov states and introduces feasibility cuts, can properly address large-scale financial planning problems.