Decomposition and approximation techniques for large-scale multistage stochastic programs: with applications in finance

Abstract

In this dissertation, we study decomposition and approximation techniques to solve a large-scale financial planning problem in multistage stochastic program.First, we propose an extended framework of the state-of-the-art stagewise decomposition algorithm called stochastic dual dynamic programming (SDDP) tailored for large-scale financial planning problems. Our proposed framework addresses the limitations of conventional SDDP in a perspective of finance, making it a viable tool for solving large-scale financial planning problems.Second, we apply the proposed SDDP framework to the asset liability management (ALM) problem of National Pension Service (NPS) of Korea. Furthermore, a sensitivity analysis under various contribution related parameters is conducted to provide insightful information for the sustainability of Korean public pension fund.Last, we introduce a novel stagewise decomposition algorithm called value function gradient learning (VFGL). Throughout three numerical examples, we verify that the VFGL has a great numerical potential compared to the conventional stagewise decomposition algorithms.The findings in this study will provide better understanding and techniques to solve large-scale financial planning problem, and further to the general large-scale multistage stochastic programs.