Solving this in mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg128054] Solving this in mathematica?
• From: Leon <leon.he88 at gmail.com>
• Date: Wed, 12 Sep 2012 02:58:24 -0400 (EDT)
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• Delivered-to: l-mathgroup@wolfram.com
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```I have following code in mathematica:

------------------------------------------------------------
rbar = 0.006236
rt = r_bar
k = 0.95
sigmar = 0.002
betazr = -0.00014
sigmaz = 0.4
pi = 0.99
chi = 0.05
Cbar = -3.7

alpha1[n_] := alpha1[n] = alpha1[n - 1] + alpha2[n - 1]
alpha2[n_] := alpha2[n] = k (alpha2[n - 1])
sigma1sq[n_] :=
sigma1sq[n] = sigma2sq[n - 1] + 2 sigma12[n - 1] + sigmaz^2
sigma12[n_] :=
sigma12[n] = k (sigma12[n - 1]) + k (sigma2sq[n - 1]) + betazr
sigma2sq[n_] := sigma2sq[n] = (k^2) (sigma2sq[n - 1]) + sigmar^2
phi1[n_] := phi1[n] = phi1[n - 1] + phi2[n - 1] + (0.5) (sigmaz^2)
phi2[n_] := phi2[n] = k (phi2[n - 1]) + (1 - k) (rbar)
psi[n_] := psi[n] = phi1[n] - (0.5) (sigma1sq[n])

alpha1[0] = 0
alpha2[0] = 1
sigma1sq[0] = 0
sigma12[0] = 0
sigma2sq[0] = 0
phi1[0] = 0
phi2[0] = 0

B[h_, r_] := Exp[(-alpha1[h]) (r) - psi[h]]
Exp[Cbar - beta] Sum[(Pi^x) B[x, r], {x, 1, 1000}]

----------------------------------------------------------------------

and I am wondering if it is possible to solve the last line such that I have "r" as a function of "beta", satisfying

Exp[Cbar - beta] Sum[(Pi^x) B[x, r], {x, 1, 1000}] = 1

Because ultimately, I would need to integrate a function J[r] over "beta", so if I don't have "r" as a function of "beta", I don't know how to do the integration of J[r].

Thank you!! L.

```

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