Occurrence in the XIV century financial mathematics and the formation of risk category on the material of trading books of the late Middle Ages and Renaissance

In the late Middle Ages in Mediterranean republics owing to trading activity the terminology and the basic structure of financial mathematics originated and developed. The cashless calculation and the corresponding financial documents emerged in the direction of the main financial flows. The record of receipts and expenditures in double-entry book-keeping, the conversion of coins to a bank coin, the account of shares in profit and damage, calculation sums insured and the various risk-bearing forms were realized in trading books. The role of insurer arises; the concepts of insurance risk, insurance term, insurance premium as a measure of risk, insurance compensation were differentiated. Risk formalization was necessary for the insurance activity and has laid the foundation of probability. Chronicles, merchant handbooks and trading books XIII-XV c. used as sources.