Computational finance

[3] Computational finance emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses.

[7] Mathematical finance began with the same insight, but diverged by making simplifying assumptions to express relations in simple closed forms that did not require sophisticated computer science to evaluate.

[8] In the 1960s, hedge fund managers such as Ed Thorp[9] and Michael Goodkin (working with Harry Markowitz, Paul Samuelson and Robert C. Merton)[10] pioneered the use of computers in arbitrage trading.

In academics, sophisticated computer processing was needed by researchers such as Eugene Fama in order to analyze large amounts of financial data in support of the efficient-market hypothesis.

[11] In the late 1970s and early 1980s, a group of young quantitative practitioners who became known as "rocket scientists" arrived on Wall Street and brought along personal computers.

Simulation of Brownian Motion sample paths is an important tool in calculating the price of financial instruments under the risk-neutral measure .