Control of a finite dam when the input process is either spectrally positive Levy or spectrally positive Levy reflected at its infimum

TL;DR

This paper develops a unified control framework for finite dams with spectrally positive Levy input processes, employing scale functions of Levy processes to extend previous results.

Contribution

It introduces a novel approach using scale functions for controlling finite dams with Levy inputs, unifying and extending prior models.

Findings

Extended control policies to spectrally positive Levy processes.

Unified framework simplifies previous differential equation methods.

Demonstrated effectiveness of scale function techniques in dam control.

Abstract

We consider the control of a finite dam when the input process is either spectrally positive Levy or spectrally positive Levy reflected at its infimum, using P(M,Lambda,tau) control policies. Our results extend and unify the results Bea et al (2003), Lam and Lou (1987), and Attia (1987). The techniques used by the above authors involve solving systems of differential or integral equations. Our methods of proof are based on the theory and methods of scale functions of Levy processes.