There are two different papers published by Freddy Delbaen and Walter Schachermayer in 1994. ### A general version of the fundamental theorem of asset pricing - Published in [Mathematische Annalen](https://link.springer.com/article/10.1007/BF01450498) - They prove (Theorem 1.1 in the paper) that NFLVR is equivalent to the existence of at least one EMM (``First FTAP'') - In section 6, study the relationship between NFLBR, NFL and NFLVR. The gist is that NFLVR is a special case of NFLBR. Here's a quote from the paper (page 501): > *The difference between (NFLVR) and (NFLBR) is now clear. In the no > free lunch with vanishing risk property we deal with sequences such > that the negative parts tend to 0 uniformly. In the no free lunch with > bounded risk property we only require these negative parts to tend to > 0 in probability and remain uniformly bounded!* - Thus, NFLBR $\Leftarrow$ NFLVR $\Leftrightarrow$ EMM exists. The version of the FTAP from Delbaen and Schachermayer is amongst the most general versions of the first FTAP. The original ideas trace back to [Ross (1978)](https://www.jstor.org/stable/2352277) and [Harrison and Kreps (1979)](https://www.sciencedirect.com/science/article/abs/pii/0022053179900437). ### Arbitrage and free lunch with bounded risk for unbounded continuous processes - Published in [Mathematical Finance]( https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9965.1994.tb00063.x) - They give an example of a market without arbitrages that does not have an EMM (example 2 in the paper). NFLBR is satisfied though. Thus, this paper presents a counterexample to NFLBR $\Rightarrow$ EMM exists. Local martingale measures are more closely linked to NFLBR. - NFLBR has also been used in other earlier papers. - [Back and Pliska (1991)](https://www.sciencedirect.com/science/article/abs/pii/030440689190014K) also give an example of an arbitrage-free market without an EMM.