Consider the non linear inequality $\sum_{i=1}^{n}a_{i}u^{\sum\limits_{j=1}^{i}y_j} > c$ $y_j \in \{0,1\}, j=1,2,\dots,n$ $a_i \in \mathbb{R}, i=1,2,\dots,n$ $n \in \mathbb{N}, u>0, c > 0$ where the $y_j$ are variables and all other term constant. Is there a way to find the solution space analytically?
The inequality arises as follow: start with a geometric Brownian motion process $(S_t)_{t \geq 0}$, approximate it by a binomial process, define the random variable $X=\sum\limits_{i=1}^{n}a_iS_n/S_{i-1},n \in N$, evaluate $E(\max(X,c)), c>0$. The inequality is an attempt to calculate how many terms are involved in the limited expectation