To supplement replacement income provided by Social Security and employer­sponsored pension plans, individuals need to rely on their own saving and investment choices during accumulation. Once retired, they must also decide at which rate to spend their savings, with the usual dilemma between...

Abstract Starting from the requirement that risk of financial portfolios should be measured in terms of their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize convex loss-based risk measures by a...

Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a 'risk measure' that summarizes the risk of the portfolio. We define the notion of 'risk measurement procedure', which includes both of...