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Question:

I live in Israel and trade on the NY Stock Exchange. One type of trade is a limit trade order. One sets a target price for a stock. When it reaches the target price, the trade (buy or sell) takes place. May I place such an order on Friday, as most of the market day in NY is during Shabbat in Israel?

Answer: Usually, a non-Jew who is paid by the job may do such work for a Jew on Shabbat, as he is considered to be working on his own behalf for the pay. However, he may not be told to do the work on Shabbat (Shulchan Aruch, Orach Chayim 247:1). In this case, your instructions are that if the limit is reached on Shabbat, they should make the transaction specifically then.
We have ascertained that after you place the order by computer, there is rarely human intervention in the processing of your trade. When no melacha is being done on Shabbat on your behalf by a person, but only automatic computer activity, the main question disappears. Someone at your brokerage may do melacha in sending you confirmation notification. On the other hand, even if this does happen, you do not need to ask them to do so on Shabbat.
However, there is a much broader basis for not being concerned even in a case where work would be done on Friday. The final bell on the NYSE is at 4:00 PM and the earliest sunset in NY is 4:28 PM. Thus there is no stock activity work on Shabbat. The question, though, is whether the important thing is that they do work before Shabbat at their location or that the work they do for you is not on Shabbat at your location.
We start with the following halacha that the Rashba (accepted by the Shulchan Aruch, Orach Chayim 263:17) inferred from Shabbat 151a. If one accepts Shabbat early, he may ask a fellow Jew who did not yet accept Shabbat to do work on his behalf. This is surprising since after accepting Shabbat, one is supposed to act as if it is Shabbat, and if one cannot ask a non-Jew to do work for him on Shabbat, it should be forbidden to ask a Jew to do work. Three main distinctions are made: 1) The prohibition to ask others was not instituted when one had a way (and, in some cases, still does) to not be forbidden to do the work himself (Beit Yosef, ad loc.); 2) When one accepts Shabbat, he only accepts prohibitions that he performs himself (Levush 263:17); 3) There is no prohibition to ask someone else when that which he requests is not a melacha for the person requested (Taz 263:3). The Taz’s approach is strongest and most accepted (see Mishna Berura 263:64; Minchat Shlomo I, 19; Ta’arich Yisrael 8). Therefore, even though the work will be done when it is Shabbat for the requester, since for the person doing it, it is not a violation of Shabbat, it is permitted to carry out the work.
There is still a problem. R. Akiva Eiger (Shut I, 19) says that even when the practical dealings are complete before Shabbat, one may not have a transaction take effect on Shabbat. Therefore, ostensibly, even though nothing is being done wrong on Shabbat, the fact that the transaction may be going through on Shabbat should be a problem. However, R. Akiva Eiger’s idea is so novel that many poskim disagree with it and others limit it to cases similar to the contexts which are the basis of his idea. Thus, his concern need not be applied here (see discussion in Bemareh Habazak V, 37:(21)).
The following observation is of critical importance. If one prohibits the described trade orders on Friday because it will likely happen on Shabbat for the owner, then there are even stronger grounds to require the following stringency. While the owner of a kosher bakery in NY is visiting Israel, the bakery must be closed 7 hours before Shabbat. As several poskim point out, we have never heard of such a chumra being employed, and we have given a basis why it is unnecessary. The same logic can be employed to permit the less severe case of an automatic transaction on amorphous entities known as shares.