This paper proposes a new kind of asymmetric GARCh where the conditional variance obeys two different regimes with a smooth transition function. In one formulation, the conditional variance reacts differently to negative and positive shocks while in a second formulation, small and big shocks...

The authors examine a variant of the uncapacitated lot-sizing model of Wagner-Within involving sales instead of fixed demands, and lower bounds on stocks. Two extended formulations are presented, as well as a dynamic programming algorithm and a complete description of the convex hull of solutions.