Economics Insights @ CBS

Special algorithms have been developed to compute an optimal (s,S) policy for an inventory model with discrete demand and under standard assumptions (stationary data, a well-behaved one-period cost function, full backlogging and the average cost criterion). We present here an iterative algorithm for continuous demand distributions which avoids any form of prior discretization. The method can be viewed as a modified form of policy iteration applied to a Markov decision process with continuous state space. For phase-type distributions, the calculations can be done in closed form.

This paper analyzes the empirical behavior of stock-return volatilities prior to and subsequent to the ex-dates of stock splits. The evidence demonstrates rather unambiguously that there is, on the average, an approximately 30% "arbitrary" increase in the return standard deviations following the ex-date. The increase holds for both daily and weekly data, and it is not temporary. No explanatory confounding variables, such as institutional frictions affecting price observations, have been identified.

Let P be a polytope in Rⁿ containing the origin in its interior, and let P* be the algebraic dual polytope of P. Let Q Rⁿ x [0,1] be the (n+1)-dimensional polytope that is the convex hull of P x {1} and P* x {0}.