In
financial mathematics
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.
In general, there exist two separate branches of finance that require ...
and
economics
Economics () is the social science that studies the production, distribution, and consumption of goods and services.
Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...
, a distortion risk measure is a type of
risk measure
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions, such as bank ...
which is related to the
cumulative distribution function of the
return of a
financial portfolio
In finance, a portfolio is a collection of investments.
Definition
The term “portfolio” refers to any combination of financial assets such as stocks, bonds and cash. Portfolios may be held by individual investors or managed by financial pro ...
.
Mathematical definition
The function
associated with the
distortion function
A distortion function in mathematics and statistics, for example, g: ,1\to ,1/math>, is a non-decreasing function such that g(0) = 0 and g(1) = 1. The dual distortion function is \tilde(x) = 1 - g(1-x). Distortion functions are used to define ...