Individuals, endowments and trusts face uncertain lifetimes. When the planning horizon of an entity is stochastic and Pareto distributed, hyperbolic discounting and time-varying consumption rates are optimal. We derive expressions for the optimal rate of consumption (draw-down) from wealth for...

We determine optimal consumption paths under a series of returns scenarios for charitable endowments with distinct tastes over investment risk and inter-temporal substitution. Charities typically prefer smooth consumption paths but are investment-risk tolerant. Using a recursive, Kreps-Porteus...

In this paper, the authors use the concept of the population Receiver Operating Characteristic (ROC) curve to build analytic models of ROC curves. Information about the population properties can be used to gain greater accuracy of estimation relative to the non-parametric methods currently in...

This paper assumes that the underlying asset prices are lognormally distributed, and derives necessary and sufficient conditions for the valuation of options using a Black-Scholes type methodology. It is shown that the price of a futures-style, marked-to-market option is given by Black's formula...

We propose the average F statistic for testing linear asset pricing models. The average pricing error, captured in the the statistic, is of more interest than the ex post maximum pricing error of the multivariate F statistic that is associated with extreme long and short positions and...