We study the optimal domain for the Hardy operator considered with values in a rearrangement invariant space. In particular, this domain can be represented as the space of integrable functions with respect to a vector measure defined on a δ-ring. A precise description is given for the case of the minimal Lorentz spaces.

We consider a buying–selling problem when two stops of a sequence of independent random variables are required. An optimal stopping rule and the value of a game are obtained.

This paper compares the relative efficiencies of pollution taxes, pollution standards, and the auctioning of pollution rights when the marginal damage function or marginal control cost are subject to uncertainty. In the first case, we find that all instruments yield the same expected social surplus. In the latter case, the choice of the optimal instrument depends, in general, on the relative el...

We consider a free boundary problem modeling growth and dissolution of a crystal in radial geometry with time-dependent data at the outer boundary. Well-posedness is shown rst for in H 1 but then, motivated by an opimal control problem, for in L 2 .

This paper provides an axiomatic foundation for a particular type of preference shock model, called the random discounting representation, where a decision maker believes that her discount factors change randomly over time. For this purpose, we formulate an infinite horizon extension of Dekel, Lipman, and Rustichini (2001), and identify the behavior that reduces all the subjective uncertainties...

Optimal control is concerned with achieving a desired outcome, not by manipulating the path that can be taken within a specific system, but by manipulating the forces, or controls, that are fundamental to the system. It has no doubt been shown in the previous paper in this SSP series that optimal control problems are expressed using the functional, J, which serves as the performance index, in t...

For a system subject to breakdown at some random time two continuous surveillance plans are available, diiering in eeciency and cost. The controller is allowed to switch from one plan to the other at any time. We nd the optimal surveillance strategy in closed form and apply this result in some examples.