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Maximizing Recursive Functions

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  • Subject: [mg20981] Maximizing Recursive Functions
  • From: "Christopher Knittel" <knittel at>
  • Date: Wed, 1 Dec 1999 01:50:52 -0500 (EST)
  • Organization: Boston University
  • Sender: owner-wri-mathgroup at

Hello all,

I am trying to maximize a recursive function. The basic structure is as

The recursive part is as follows:

fii[ti_ n_]:=(1-ti)*fii[ti n-1]
foi[to_ n_]:=(1-to)*g[ti n-1]
g[ti_ to_ n_]:=ti*(fii[ti n-1]+foi[ti n-1])+to*g[ti n-1]
fii[ti_ 1]:=(1-ti)
foi[ti_ 1]:=0
g[ti_ 1]:=ti

So 'to' and 'ti' are choice variables that are chosen in order maximize the
objective function. QUESTION: Should I have fii[ti_ n_] or fii[n_]? The
objective function is as follows:

po[to_  c_]:=(100*to-25)*25
pii[ti_ c_]:=((100*(1+ti)-50)*50-25*c)
poi[ti_ c_ k_]:=((100*(1+ti)-50)*50-25*c-k)
EP[to_ ti_ c_ k_ d_ ] := [Sum]*(d^(n - 1))*((fii[n]*pii[ti c] +
foi[n]*poi[ti c k] + g[n]*po[to c]))

The summation part is done with the symbols in Mathematica so this part is
correct even though it doesn't look so. The actual summation is from 1 to
infinity, but Mathematica can't handle this. How far can I go?

My questions are when I should use x or x_. Again I want to choose 'to' and
'ti' to maximize EP.

Thanks in advance for your help,

Christopher Knittel
Department of Finance and Economics    Email: knittel at
Boston University                                    Office: 617.353.2036
595 Commonwealth Ave                         Fax: 617.353.6667
Boston, MA 02215                                 Webpage:

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