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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Gao, Wenjie"],"institution":null,"degree_name":"Mathematics, PhD","degree_level":"Restricted to Claremont Colleges Dissertation","degree_discipline":"Institute of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Allon Percus","Jamie Haddock"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-01-01T08:00:00Z","date_published":"2024-01-01T08:00:00Z","updated_at":"2026-07-24T01:41:01Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarship.claremont.edu/cgu_etd/901","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Allon Percus","Jamie Haddock"]},{"key":"dc:creator","label":"Author","values":["Gao, Wenjie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2027-01-13T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Institute of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Restricted to Claremont Colleges Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics, PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarship.claremont.edu/cgu_etd/901"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Variable Annuity -- Laps Behavior"]}]}],"canonical_facts":{"dc:contributor":["Allon Percus","Jamie Haddock"],"dc:creator":["Gao, Wenjie"],"dc:date.available":["2027-01-13T08:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://scholarship.claremont.edu/cgu_etd/901"],"dc:subject":["Mathematics"],"dc:title":["Variable Annuity -- Laps Behavior"],"thesis:degree_discipline":["Institute of Mathematical Sciences"],"thesis:degree_level":["Restricted to Claremont Colleges Dissertation"],"thesis:degree_name":["Mathematics, PhD"]},"updated_at":"2026-07-24T01:41:01Z"}