Underwriters of annuity products and administrators of defined-benefit pension plans with periodic payments are under financial obligation to their policyholders or participants until the death of the counterparty. Hence, the underwriters would be subject to longevity risk should the average lifespan of the entire population increase to an unforeseen level. Meanwhile, the fact that the effective federal funds rate is at its historic low level implies that the present value of life-contingent cash outflows for insurers is subject to the greatest amount of longevity risk. As a benchmark mortality model in the insurance industry is the Lee-Carter model, in this dissertation we summarize some flaws of model assumptions and the model's classical inference method. Based on the understanding of these flaws, 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 relatively small sample. Then we propose a 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 the mortality index and apply it to a bivariate dataset of U.S. mortality rates. Finally, we conclude the dissertation by arguing that the proposed model is adequate and by suggesting some potential hedging practices based on that.