Consider a discrete stochastic process $\{X_t\}_{t \in T}$ with the following properties. Each $t \in T$ has a value $v(t) \in \mathbb{R}_{+}$ and the value is added to the overall value conditioned on some event $\mathbb{1}_t = 1$; that is, $X_t = v(t) \cdot \mathbb{1}_t$. In addition, for every $t \in T$ the expected value added by the next increase after $t$ is bounded by one, that is: Let $n(t)$ be the first time $s$ after time $t$ in which $\mathbb{1}_s = 1$, then assume that $\mathbb{E} [X_{n(t)}] \leq 1$ for all $t \in T$.
Question: Using what we know on $X_{n(t)}$, can we give an upper bound on the expected value of a single added value, that is $\mathbb{E} \left[ \frac{\sum_{t \in T} X_t}{\sum_{t \in T} \mathbb{1}_t}\right]$?
Any pointer or help would be highly appreciated.