Data Science
Permanent URI for this collectionhttps://uwspace.uwaterloo.ca/handle/10012/18081
This is the collection for the University of Waterloo's Data Science program.
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Browsing Data Science by Subject "neural network"
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Item Optimal Decumulation for Retirees using Tontines: a Dynamic Neural Network Based Approach(University of Waterloo, 2023-09-19)We introduce a new approach for optimizing neural networks (NN) using data to solve a stochastic control problem with stochastic constraints. We utilize customized activation functions for the output layers of the NN, enabling training through standard unconstrained optimization techniques. The resulting optimal solution provides a strategy for allocating and withdrawing assets over multiple periods for an individual with a defined contribution (DC) pension plan. The objective function of the control problem focuses on minimizing left-tail risk by considering expected withdrawals (EW) and expected shortfall (ES). Stochastic bound constraints ensure a minimum yearly withdrawal. By comparing our data-driven approach with the numerical results obtained from a computational framework based on the Hamilton-Jacobi-Bellman (HJB) Partial Differential Equation (PDE), we demonstrate that our method is capable of learning a solution that is close to optimal. We show that the proposed framework is capable of incorporating additional stochastic processes, particularly in cases related to the use of tontines. We illustrate the benefits of using tontines for the decumulation problem and quantify the decrease in risk they bring. We also extend the framework to use more assets and provide test results to show the robustness of the control.Item A Robust Neural Network Approach to Optimal Decumulation and Factor Investing in Defined Contribution Pension Plans(University of Waterloo, 2023-09-18)In this thesis, we propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. The NN utilizes customized output layer activation functions, which permits training via standard unconstrained optimization. The optimal solution of the two-asset problem yields a multi-period asset allocation and decumulation strategy for a holder of a defined contribution (DC) pension plan. The objective function of the optimal control problem is based on expected wealth withdrawn (EW) and expected shortfall (ES) that directly targets left-tail risk. The stochastic bound constraints enforce a guaranteed minimum withdrawal each year. We demonstrate that the data-driven NN approach is capable of learning a near-optimal solution by benchmarking it against the numerical results from a Hamilton-Jacobi-Bellman (HJB) Partial Differential Equation (PDE) computational framework. The NN framework has the advantage of being able to scale to high dimensional multi-asset problems, which we take advantage of in this work to investigate the effectiveness of various factor investing strategies in improving investment outcomes for the investor.