When faced with death counts strati ed by age, analysts often calculate a crude mortality rate (CMR) as a single summary measure. This is done by simply dividing total death counts by total population counts. However, the crude mortality rate is not appropriate for comparing different populations due to the significant impact of age on mortality and the possibility of having different age structures for different populations. While a set of age-adjustment methods seeks to collapse age-specific mortality rates into a single measure that is free from the confounding effect of age structure, we focus on one of these methods called "direct age-standardization" method which summarizes and compares age-specific mortality rates by adopting a reference population. While qualitative insights in relation to age-standardization are often discussed, we seek to approximate age-standardized mortality rate of a population based on the corresponding CMR and the 90th quantile of its population distribution. This approximation is most useful when age-specific mortality data is unavailable. In addition, we provide quantitative insights related to age-standardization. We derive our model based on mathematical insights drawn from the explication of exact calculations and validate our model by using empirical data for a large number of countries under a large number of circumstances. We also extend the application of our approximation model to other age-standardized mortality indicators such as cause-specific mortality rate and potential years of life lost. In the second part of the thesis, we consider the formulation of a general risk management procedure, where risk needs to be measured and further mitigated. The formulation admits an optimization representation and requires as input the distributional information about the underlying risk factors. Unfortunately, for most risk factors it is known to be difficult to identify their distribution in full details, and more problematically the risk management procedure can be prone to errors in the input distribution. In particular, one of the most important distribution information is the covariance hat captures the spread and correlation among risk factors. We study the issue of covariance uncertainty in the problem of mitigating tail risk and by admitting an uncertainty set of covariance of risk factors, we propose a robust optimization model which minimizes risk for the worst scenario especially when data is insufficient and the number of risk factors is large. We will then transform our model into a computationally solvable one and test the model using real-world data.