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Friday, January 24, 2020

**Abstract:** Underwriters of annuity products and administrators of pension funds are under ﬁnancial obligation to their policyholder until the death of counterparty. Hence, the underwriters are subject to longevity risk when the average lifespan of the entire population increases, and yet, such risk can be managed through hedging practices based on parametric mortality models. As a benchmark mortality model in insurance industry is Lee-Carter model, we ﬁrst summarize some ﬂaws regarding the model and inference methods derived from it. Based on these understandings we propose a modiﬁed Lee-Carter model, accompanied by a rigorous statistical inference with asymptotic results and satisfactory numerical and simulation results derived from a small sample. Then we propose bias corrected estimator which is consistent and asymptotically normally distributed regardless of the mortality index being a unit root or stationary AR(1) time series. We further extend the model to accommodate AR(2) process for mortality index, and, a bivariate dataset of U.S. mortality rates. Finally, we conclude by a detailed model validation and some discussions of potential hedging practices based on our parametric model.