arXiv subjects

Kenneth Q. Zhou

Publications and source records attributed to Kenneth Q. Zhou.

8 recordsLinked to original sources

arXiv2026

A Tale of Two Pathways to Gompertz Mortality: Reliability and Vitality from an Actuarial Perspective

This paper studies two mechanistic explanations for human mortality by examining reliability theory and vitality modelling through a unified actuarial perspective. While the two approaches arise from different ageing mechanisms, we show that both can naturally generate the Gompertz law under suitable assumptions and can be extended to produce the Makeham law and late-life mortality plateaus. Using Canadian mortality data, we investigate the empirical behaviour of each approach and highlight the roles of heterogeneity, extrinsic risk, and stochastic randomness. Furthermore, we develop parallel definitions of biological age under both approaches and analyse how subjective survival beliefs emerge from misspecified parameters. Our comparison of these two approaches provides actuarial insights into the natural foundations of Gompertz mortality and the interpretation of ageing, frailty and death.

stat.OT↗

arXiv2026

Mortality Heterogeneity and Actuarial Fairness in China's Notional Defined Contribution Pension System

We study actuarial fairness in China's notional defined contribution (NDC) pension system when mortality differs across income groups. Under current rules, individual account balances are converted into monthly benefits using an official annuity divisor that depends only on retirement age. We develop a mortality-differentiated Lee-Carter framework with group-specific baseline mortality schedules and a common period effect, estimated by combining national mortality data for 1994-2020 with CHARLS subgroup data for 2011-2020. To model cross-group mortality parsimoniously under limited data, we parameterize the baseline schedules using Hermite splines. Applying the model to China's NDC system, we find substantial actuarial unfairness in the current age-only divisor. The subsidy rises monotonically with income, implying both an aggregate actuarial shortfall and a reverse transfer from poorer to richer retirees. We then compare four implementable income-dependent annuitization rules, ranging from a simple bracket design to marginal-rule alternatives, and show that all substantially reduce the reverse transfer.

q-fin.RM↗

arXiv2026

The Long Shadow of Pandemic: Understanding the lingering effects of cause-specific mortality shocks

In the aftermath of the COVID-19 pandemic, empirical data have revealed that large-scale health crises not only cause immediate disruptions in mortality dynamics but also have persistent effects that may last for several years. Existing mortality models largely assume that mortality shocks are transitory and overlook how their effects can be long-lasting and heterogeneous across age groups and causes of death. In response to this limitation, we propose a novel stochastic mortality model that captures age- and cause-specific long-lasting effects of mortality jumps through a gamma-density-like decay function, estimated via a customized conditional maximum likelihood algorithm. Applying the model to recent U.S. mortality data, we reveal divergent persistence patterns across demographic groups and provide key insights into the tail risk profiles of life insurance and annuity products. Our scenario-based analyses further show that neglecting persistent shock effects can lead to suboptimal hedging, while the proposed model enables what-if testing to analyze such effects under potential future health crises.

stat.AP↗

arXiv2026

Fair Pricing in Long-Term Insurance: A Unified Framework

Extant literature on fair pricing methods for actuarial contexts has primarily focused on the regression setting. While such approaches are well-suited to short-term products, it is unclear how they generalize to long-term products, whose pricing essentially relies on estimating transition rates in multi-state models. To address this gap, we propose a unified framework that recasts the estimation of any given multi-state transition model as a set of Poisson regression problems. This reformulation enables the direct application of existing fair pricing methods, which together constitute our proposed methodology. As an illustration, we apply the framework to a fair pricing exercise for a stylized long-term care insurance product using data from the University of Michigan Health and Retirement Study (HRS), focusing on a post-processing approach. We further explain how the framework readily accommodates pre-processing and in-processing fairness methods.

q-fin.PR↗

arXiv2025

A Natural Hedging Framework for Longevity Risk with Graphical Risk Assessment

Natural hedging allows life insurers to manage longevity risk internally by offsetting the opposite exposures of life insurance and annuity liabilities. Although many studies have proposed natural hedging strategies under different settings, calibration methods, and mortality models, a unified framework for constructing and evaluating such hedges remains undeveloped. While graphical risk assessment has been explored for index-based longevity hedges, no comparable metric exists for natural hedging. This paper proposes a structured natural hedging framework paired with a graphical risk metric for hedge evaluation. The framework integrates valuation, calibration, and evaluation, while the graphical metric provides intuitive insights into residual dependencies and hedge performance. Applied to multiple hedging scenarios, the proposed methods demonstrate flexibility, interpretability, and practical value for longevity risk management.

q-fin.RM↗

arXiv2025

Mortality Modeling and Forecasting with the Actuaries Climate Index

Climate change poses increasing challenges for mortality modeling and underscores the need to integrate climate-related variables into mortality forecasting. This study introduces a two-step approach that incorporates climate information from the Actuaries Climate Index (ACI) into mortality models. In the first step, we model region-specific seasonal mortality dynamics using the Lee-Carter model with SARIMA processes, a cosine-sine decomposition, and a cyclic spline-based function. In the second step, residual deviations from the baseline model are explained by ACI components using Generalized Linear Models, Generalized Additive Models, and Extreme Gradient Boosting. To further capture the dependence between mortality and climate, we develop a SARIMA-Copula forecasting approach linking mortality period effects with temperature extremes. Our results show that incorporating ACI components systematically enhances out-of-sample accuracy, underscoring the value of integrating climate-related variables into stochastic mortality modeling. The proposed framework offers actuaries and policymakers a practical tool for anticipating and managing climate-related mortality risks.

stat.AP↗

arXiv2025

Modeling Excess Mortality and Interest Rates using Mixed Fractional Brownian Motions

Recent studies have identified long-range dependence as a key feature in the dynamics of both mortality and interest rates. Building on this insight, we develop a novel bi-variate stochastic framework based on mixed fractional Brownian motions to jointly model their long-memory behavior and instantaneous correlation. Analytical solutions are derived under the risk-neutral measure for explicitly pricing zero-coupon bonds and extreme mortality bonds, while capturing the impact of persistent and correlated risk dynamics. We then propose a calibration procedure that sequentially estimates the model and risk premium parameters, including the Hurst parameters and the correlation parameter, using the most recent data on mortality rates, interest rates, and market conditions. Lastly, an extensive numerical analysis is conducted to examine how long-range dependence and mortality-interest correlation influence fair coupon rates, bond payouts and risk measures, providing practical implications for the pricing and risk management of mortality-linked securities in the post-pandemic environment.

q-fin.RM↗

arXiv2024

A new paradigm of mortality modeling via individual vitality dynamics

The significance of mortality modeling extends across multiple research areas, ranging from life insurance valuation to optimal lifetime decision-making. Existing approaches, such as mortality laws and factor-based models, often fall short in capturing the complexity of individual mortality, hindering their ability to address specific research needs. To overcome these limitations, this paper introduces a novel approach to mortality modeling centered on the dynamics of individual vitality. A four-component framework is developed to account for initial conditions, natural aging processes, stochastic fluctuations, and accidental events over an individual's lifetime. We demonstrate the framework's analytical capabilities across various settings and explore its practical implications in solving life insurance problems and deriving optimal lifetime decisions. Our results show that the proposed framework not only encompasses existing mortality models but also provides individualized mortality outcomes and offers an intuitive explanation for survival biases.

stat.AP↗