The question is leading, so I will address a few parts separately and I apologize for the length:
The Middle Ages is the period from 400-1400 AD. The occupation choices of Jews changed dramatically during this 1,000 year period, especially around the 7th century. The question also asks about the time period from 1300-1700 AD. During 1300-1700, only 5-10% of European Jews were farmers, the main occupation of the time period. It's not clear exactly how many European Jews were engaged in finance, but over 50% is possible. A higher percent seems economically impossible, even if all occupation choices were closed except finance as became the case by 1700, since Jews were restricted to ghettos and had separate micro-economies. They had separate schools, religious leaders, scholars, doctors, merchants, and food service providers.
Almost all Jews were farmers in the first half of the first millennium, whereas at the end of the first millennium a small proportion of them remained in agriculture and the greatest majority became craftsmen, artisans, merchants, doctors, and moneylenders. A shift is also seen away from craftsmen, merchants and artisans towards a greater proportion of money-lenders over time. I will propose a few reasons for this.
The negative stereotype of Jews in finance is that they are tight-fisted or greedy. Shylock is after his "pound of flesh." Usury was forbidden to Christians, so people of the era viewed the occupation as sinful and evil due to their religion. There are dozens of instances of Jewish laws regulating ethical financial behavior.
The Wikipedia article states the theory that Jews chose the occupation of finance and money-lending due to restrictions in other occupations. This is likely only partially correct. Oliver Cromwell introduced the first blanket occupational restrictions on Jews anywhere in Europe in the 17th century, but Jews were well-established in finance by this time. The restrictions were a political move to convince Parliament to allow Jews to re-enter the country after their expulsion in the 13th century, since he was seeking help from Jewish bankers. It was common for them to be excluded from guilds, so they might not be able to be craftsmen or artisans. The Jewish Virtual Library says that Christians often complained that Jews were overly aggressive and did not follow the business etiquette of the times, so their business practices were sometimes regulated or they might be banned from some areas of business entirely.
Another widely accepted theory for the large numbers of Jews in finance is a change in religious education that increased literacy rates during the Talmudic era. According to this theory, Jews changed from a primarily agricultural people to primarily urban people engaged in trade, finance, commerce and medicine at roughly the same time, around 7th century, in different areas throughout the world, despite varied treatment in occupation restrictions. It is also shown that Jews that remained farmers tended to convert to Islam or Christianity at much higher rates than urban Jews, while effective laws were passed to prevent conversion
of Christians to Jews starting in the 5th century.
According to Botticini and Eckstein: "The transition away from agriculture into crafts, trade, and moneylending started in the Talmudic period, especially in Babylon. The Babylonian Talmud (redacted in about 500 CE) has many more debates and rulings regarding crafts and trade than the Talmud of the Land of Israel. In the fifth—sixth centuries the Jews abandoning agriculture moved to the towns and became small shopkeepers and artisans in the tanning, linen, silk, dyeing industries, and glassware making"
In Babylon, its known that two banks were established by Jews as well. So also during the Talmudic Period, finance was an established occupation but small. Finance was well-established as a Jewish profession by 1170 as documented by the travels of Benjamin of Tudela and the laws of Talmud.
Persecution of the Jews worsened over time, so it reasons that laws restricting occupations for instance became more frequent and more restrictive with effects on occupational choices. At the beginning of the Middle Ages, the Jews were viewed as the "Chosen People" by Christians, so although popular sentiment was often against them, Catholic Church leaders protected their rights. The Crusades hardened attitudes and the establishment of universities in the 13th century led to Christian scholars examining Jewish holy texts. Church leaders decided the Talmud was a heresy within their purview to regulate. This turbulent time period of persecution coincides with the rise of powerful European financial centers, such as Venice in the 14th century, through the work of Jewish bankers.
The Jewish Emancipation started in the late 18th century and ended in the late 20th century. Although Jews are still over-represented in the field of finance, it is not as pronounced as it once was.
References:
William Shakespeare. The Merchant of Venice.
Jewish ghettos in Europe. Wikipedia
Economic Antisemitism. Wikipedia
Venice: Wall Street of the Middle Ages
Middle Ages. Wikipedia
Banking and Bankers. Jewish Virtual Library
Church and the Jews in the Middle Ages. Catholic Culture.org
Jewish Emancipation. Wikipedia
Maristella Botticini and Zvi Eckstein. Jewish Occupational Selection: Education, Restrictions, or Minorities?
Resettlement of the Jews in England. Wikipedia
Maristella Botticini and Zvi Eckstein. From Farmers to Merchants:A Human Capital Interpretation of Jewish Economic History
