Skip to main content
Article thumbnail
Location of Repository

A Proof of the Bomber Problem's Spend-It-All Conjecture

By Jay Bartroff

Abstract

The Bomber Problem concerns optimal sequential allocation of partially effective ammunition $x$ while under attack from enemies arriving according to a Poisson process over a time interval of length $t$. In the doubly-continuous setting, in certain regions of $(x,t)$-space we are able to solve the integral equation defining the optimal survival probability and find the optimal allocation function $K(x,t)$ exactly in these regions. As a consequence, we complete the proof of the "spend-it-all" conjecture of Bartroff et al. (2010b) which gives the boundary of the region where $K(x,t)=x$

Topics: Mathematics - Probability, Mathematics - Statistics Theory, 60G40, 62L05, 91A60
Year: 2011
OAI identifier: oai:arXiv.org:1103.0309
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/1103.0309 (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.