Influence of mathematical models in finance on practice: past, present and future

The mathematics of finance contains some of the most beautiful applications of probability and optimization theory. Yet despite its seemingly abstruse mathematics, finance theory over the last two decades has found its way into the mainstream of finance practice. Today much of the applied financial research on the use of mathematical models takes place within financial institutions. It was not always thus. The scientific breakthroughs in financial modelling both shaped and were shaped by the extraordinary flow of financial innovation which coincided with revolutionary changes in the structure of world financial markets and institutions during the past two decades. The paper covers that development with a focus on the future role of mathematical models in finance practice.