Mathematical Applications in Quantitative Finance

Posted on November 14, 2023  •  1 minutes  • 150 words

This paper volume popularized the application of mathematics in quantitative finance, common modeling methods, and common mathematical tools in quantitative finance.

What are the different types of Mathematics found in quantitative finance?

The field of mathematics most used in quantitative finance are those of probability theory and differential equations. And,of course, numerical methods are usually needed for producing numbers.

Here‘s a list of the various approaches to modelling and a selection of useful tools. The distinction between a ‘modelling approach’ and a ’tool’ will start to become clear.

• Modelling approaches:
  • Probabilistic
  • Deterministic
  • Discrete: difference equations
  • Continuous: differential equations
• Useful tools
  • Simulations
  • Discretization methods
  • Approximations
  • Asymptotic analysis
  • Series solutions
  • Green’s functions

While these are not exactly arbitrary lists, they are certainly open to some criticism or addition. Let’s first take a look at the modelling approaches.

[1] Wilmott，M 2009 Frequently Asked Questions In Quantitative Finance, second edition. John Wiley & Sons,Ltd.