# Algorithm

## Contents

## Definition

An **Algorithm** in risk management context is a precise quantitative procedure for solving a mathematical problem (possibly in a number of steps) which produces an intermediate or final outcome that is used to support further actions. Algorithms are typically implemented in software.

In risk management, algorithms will typically be the core components (building blocks) for more complex quantitative risk models.

## Relevance for Model Performance

Algorithms may constitute a significant component of the computational budget of a risk model in terms of computer memory requirements or computational power requirements.

## Relevance for Model Risk

Established general purpose algorithms are typically well documented in academic literature and may have reference implementations in established software libraries. Use of such algorithms is an effective means of providing quality assurance regarding the fitness for purpose of these as building blocks for larger risk models.

More generally, the suitability, possible adaptations, manner of implementation, testing and documentation of algorithms are all aspects linked to possible Model Risk of quantitative risk models and hence should be part of the model validation process for such models.

## Categories of Algorithms

Large families of algorithms with similar characteristics may be implemented inside software packages, e.g. for time-series or statistical analysis.

- General Purpose
- Root Finding (1D, Multi-Dimensional)
- Sorting
- Special Functions

- Linear Algebra
- Cholesky Decomposition
- Singular Value Decomposition

- Random Number Generation
- Pseudo Random Numbers
- Quasi Random Numbers

- Fourier Transforms

- Statistical Algorithms / Machine Learning
- Classification
- Regression
- Neural Networks

- Optimization

- Solution of PDEs
- Implicit Solvers

## Issues and Challenges

- Black box use of complex algorithms can be significant source of risk