Maximizing Recursive Functions
- To: mathgroup at smc.vnet.net
- Subject: [mg20981] Maximizing Recursive Functions
- From: "Christopher Knittel" <knittel at bu.edu>
- Date: Wed, 1 Dec 1999 01:50:52 -0500 (EST)
- Organization: Boston University
- Sender: owner-wri-mathgroup at wolfram.com
Hello all, I am trying to maximize a recursive function. The basic structure is as follows: 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, Chris ____________________ Christopher Knittel Department of Finance and Economics Email: knittel at bu.edu Boston University Office: 617.353.2036 595 Commonwealth Ave Fax: 617.353.6667 Boston, MA 02215 Webpage: http://people.bu.edu/knittel/