Suppose I start at $A>0$ and every period I either move a distance $B$ to the right with probability $p$ or a distance $C$ to the left with probability $1-p$. The expected move is positive: $p\times B+(1-p)\times C>0$. Every period I die with probability $q$. What is the expected time before death or crossing $0$? Is there any hope for an analytical solution? Thanks.
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Clarification is in order: when you move to the right or to the left, what does "zero" represent? – Alecos Papadopoulos Nov 22 '13 at 00:12
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I meant the number 0 on the real line, so you'll cross it from the right. I hope this makes more sense. – pyanni Nov 22 '13 at 16:12