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

By Jay Bartroff


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
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