Main concepts of financial mathematics in 20–21-th centuries

Throughout the history, mathematics and finance have always been in a close relationship. Let us recall such names as Fibonacci, Pascal, Fermat, Bernoulli and others. Nevertheless, it was the doctoral dissertation of Bachelier “Theory of Speculation” in 1900 recognized as the birth certificate of the modern financial mathematics. Actually, the modern financial mathematics is an intensively developing chapter of the probability theory. We will discuss main ideas and concepts which make the background of the modern financial market theory. We point out some probabilistic methods and results that arose in connection with problems of financial mathematics.