Consider the function
\begin{eqnarray} \max_{t_1,\ldots,t_p \ge 0} V(p) & = & \sum_{i=1}^p [- \alpha t_i - \beta e^{\rho - \delta^{i-1}\theta} \prod_{k=1}^i t_k^{-\delta^{i-k}\Omega}]. \end{eqnarray}
Decision variables are $t_1,\ldots,t_p$; e is the natural log base; everything else is a strictly positive parameter.
Observations
It is possible to write $\ln(t_p)$ as a linear function of $\ln(t_1),\ldots,\ln(t_{p-1})$.
The function V(p) is concave.
Since the function is concave, it is easy to solve numerically, for example using Maple's NLPSolver.
Question: Is there either (a) a closed form expression for $t_1,\ldots,t_p$ as a function of the parameters, or (b) a simple recursion between $t_i$ and $t_{i+1}$, for $1 \le i \le p-1$?
Thank you for any suggestions.