Date of Award
Fall 2024
Degree Type
Restricted to Claremont Colleges Dissertation
Degree Name
Mathematics, PhD
Program
Institute of Mathematical Sciences
Advisor/Supervisor/Committee Chair
Qidi Peng
Dissertation or Thesis Committee Member
Allon Percus
Dissertation or Thesis Committee Member
Jamie Haddock
Terms of Use & License Information
Rights Information
© 2024 Wenjie Gao
Subject Categories
Mathematics
Abstract
This dissertation presents a comprehensive exploration of mathematical models for Variable Annuities (VAs), focusing on the dynamics of policyholder behavior and the implications for pricing and risk management. VAs are complex financial instruments offering various guarantees, such as minimum death and living benefits, contingent on market performance and policyholder actions. The research initially examines traditional industry models, such as logistic regression, used to predict policyholder decisions like lapses and surrenders.Expanding beyond conventional approaches, this work introduces a novel framework that employs utility functions to model policyholder behavior more accurately. This methodology enhances the robustness of predictions by integrating a utility-based decision process into lapse modeling, aligning more closely with realistic policyholder behavior. Additionally, the study incorporates the Heston stochastic volatility model, which allows for a more nuanced treatment of market dynamics, particularly in capturing the volatility inherent in financial markets. To further refine the model, real-world data is calibrated, providing a practical application of the theoretical models. Through detailed simulations and sensitivity analyses, the Heston model demonstrates its ability to capture the effects of market volatility and risk-free rates on policyholder behavior, leading to more accurate pricing of annuity guarantees. The utility-based model, supported by real-world data calibration, shows superior predictive power, suggesting that it could be a valuable tool for insurers in managing the risks associated with variable annuity products. The findings offer significant implications for the design and pricing of VAs, contributing to the development of more sustainable products that meet the needs of both insurers and policyholders.
ISBN
9798346862574
Recommended Citation
Gao, Wenjie. (2024). Variable Annuity -- Laps Behavior. CGU Theses & Dissertations, 901. https://scholarship.claremont.edu/cgu_etd/901.
