Differential Equations


Partner, The Intertek Group


Professor of Finance, EDHEC Business School

Abstract: In financial modeling, the goal is to be able to represent the problem at hand as a mathematical function. In a mathematical function, the dependent variable depends on one or more variables that are referred to as independent variables. In standard calculus, there are two basic operations with mathematical functions: differentiation and integration. The differentiation operation leads to derivatives. When a mathematical function has only one independent variable, then the derivative is referred to as an ordinary derivative. Typically in financial applications, the independent variable is time. The derivative of a mathematical function that has more than one independent variable (one of which is typically time) is called a partial derivative. A differential equation is an equation that contains derivatives. When it contains only an ordinary derivative, it is referred to as an ordinary differential equation; when the differential equation contains partial derivatives, the differential equation is called a partial differential equation.

In nontechnical terms, differential equations are equations that express a relationship between a function and one or more derivatives (or differentials) of that function. The highest order of derivatives included in a differential equation is referred to as its order. In financial modeling, ...

Get Encyclopedia of Financial Models II now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.