First let's recapitulate:
- The market is free of arbitrage if (and only if) there exists a
martingale measure;
- The market is complete if and only if the
martingale measure is unique;
- In an arbitrage-free market, not
necessarily complete, the price of any attainable claim is uniquely
given, either by the value of the associated replicating strategy, or
by the risk neutral expectation of the discounted claim pa yoff under any of the equivalent (risk-neutral) martingale measures.
It is hard to make an assumption on the existence of an equivalent martingale measure if the market dynamics are not given (e.g. if you don't know what stochastic processs drives the underlying asset)
Showing that an equivalent martingale measure exists depends on the setting. A lot has been researched here. I can recommend the following paper that gives a decent overview.
Let $S_t$ be the stock process. If $r=0$ and if there is an equivalent martingale measure $Q$ than $S_t exp(-rt)$=$S_t$ must be a martingale (due to $r=0$ we have no discounting). Thus $\mathbb{E}^Q[S_t]=S_0$.
Let $P_t$ be the porflio we use to hedge the claim. For us to create an arbitrage $P_0=0$ and $\mathbb{P}(P_T\geq 0)=1$ at some time $T$ in the future must hold. If we were to finance $w$-shares of the stock by borrowing our portfolio would be $P_0=wS_0 - wS_0=0$. At every time $t$ in the future the expected return will be $\mathbb{E}^Q[wS_t - wS_0]=0$. Now $S_t$ is a martingale. This means that $\forall t , \mathbb{P}(S_t<S_0)>0$. For if $\mathbb{P}(S_t<S_0)=0$ for some $t$ it would follow that $\mathbb{E}^Q[S_0]<\mathbb{E}^Q[S_t]$ and $S_t$ would not be a martingale.
This means that you always have a positive probility of loss nomatter how long you keep your stock (denoted by $\forall t , \mathbb{P}(S_t<S_0)>0$) Thus the arbitrage you constructed above can not exist.
Also note that in above setting the price your instrument would be $\mathbb{E}^Q[0.01 \cdot S_\tau]=0.01 \cdot S_0=0.01 \cdot 75=0.75$. I used optional sampling here (with $\tau$ being the stopping time of $S_t$ reaching $100$).
Alose note that I use $\mathbb{E}^Q[0.01 \cdot S_\tau]$ for $0.01 \cdot S_t$ is the porfolio that replicates the payout and as you know price of the instrument equals price of hedging etc.