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Any general tips on or examples of finding interesting generating functions from recurrence relations involving minimization and maximization?

I'd imagine the case with one term of a minimization or maximization being constant is already interesting, presumably that covers pricing American style options, although no solution has jumped out at me yet.

I'm most curious about interesting generating functions for recurrences involving minimization or maximization over multiple non-constant but not terribly complex terms however.

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    $\begingroup$ Jeff- This is isn't my area, so I can't judge questions very well, but this seems like an exceptionally vague question. Do you have a particular such generating function you're interested in? As it stands, I suspect this question will be closed, so I recommend you make it a bit more specific. The how-to-ask might be helpful: mathoverflow.net/howtoask $\endgroup$
    – Ben Webster ♦
    Apr 11, 2011 at 1:09
  • $\begingroup$ What Ben said. Even one example of a recurrence relation involving minimization would be helpful. You might find something in the Graham-Knuth-Ptashnik book, Concrete Mathematics. $\endgroup$
    – Gerry Myerson
    Apr 11, 2011 at 2:13
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    $\begingroup$ What would a good answer to this question look like? What would you do with it? Gerhard "Ask Me About System Design" Paseman, 2011.04.10 $\endgroup$
    – Gerhard Paseman
    Apr 11, 2011 at 4:24
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    $\begingroup$ Maybe a better reference than GKP is Greene, Mathematics for the Analysis of Algorithms, section 2.2.1. $\endgroup$
    – Gerry Myerson
    Apr 11, 2011 at 6:08
  • $\begingroup$ Thanks Gerry! Greene has a sufficiently general example. $\endgroup$
    – Jeff Burdges
    Apr 12, 2011 at 11:41

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