Consider as in (1, Definition 2.1) a convex subset $\mathcal{X}_1$ of the set of semimartingales $\mathbb{S}$ satisfying the following properties:
- $X_0=0$
- $X_t\geq -1$ for all $t\geq 0$
- for all bounded predictable strategies $H,G\geq 0$, $X,Y\in\mathcal{X}_1$ with $H_tG_t=0$ for all $t\geq 0$ and $Z=H\dot\ X + G\dot\ Y\geq -1$, it holds that $Z\in\mathcal{X}_1$
- being closed in the Emery topology
This set represents some wealth processes, as stated in the remark after the definition: Let $S$ be a semi-martingale and set $\mathcal{X}_1:=\{\varphi\dot\ S|\varphi\text{ is }S\text{-integrable and } (\varphi\dot\ S)\geq -1)\}$
Condition 1 states, that the accumulated income of the portfolio at time zero is zero and condition 2 states, that the accumulated loss of the portfolio is bounded from below by $-1$. But what is the financial motivation of condition 3?
