Solving Stochastic Optimal Control Problems Using Fully Coupled FBSDEs: and its applications to Pension Funds

Abstract

This thesis explores the application of stochastic control techniques in a parameter study to examine the implications of climate taxes on a pension fund. The problem at hand involves modeling a pension fund comprising various assets, with a specific focus on the portfolio’s emissions and the associated tax implications. This research aims to find the optimal allocation strategies for managing the pension fund, considering both the portfolio’s performance and the impact of taxes. By utilizing stochastic control, we explore how various factors, such as risk preferences, tax regulations, and emission considerations, influence the optimal investment and consumption policies. To solve this complex problem, the BCOS method is employed to numerically tackle the fully coupled Forward-Backward Stochastic Differential Equations (FBSDEs) arising from the control problem. The BCOS method, known for its effectiveness in solving coupled FBSDEs, is applied to tackle the complexity of the problem. This numerical approach enables the exploration of different control parameters, allowing for a comprehensive parameter study. Numerical experiments are presented to illustrate the different outcomes by varying the parameters, thus revealing the dynamic nature of the solutions.