aggregate - working with compound probability distributions
What is it?
aggregate is a Python package providing fast, accurate, and expressive data structures designed to make working with probability distributions easy and intuitive. Its primary aim is to be an educational tool, allowing experimenation with complex, real world distributions. It has applications in insurance, risk management, actuarial science and related areas.
Here are just a few of the things that aggregate does well:
- Output in tabular form using Pandas
- Human readable persistence in YAML
- Built in library of insurance severity curves for both catastrophe and non catastrophe lines
- Built in parameterization for most major lines of insurance in the US, making it easy to build a “toy company” based on market share by line
- Clear distinction between catastrophe and non-catastrohpe lines
- Use of Fast Fourier Transforms throughout differentiates aggregate from tools based on simulation
- Fast, accurate - no simulations!
- Graphics and summaries following Pandas and Matplotlib syntax
- Building intuition around how loss distribtions convolve
- Convergence to the central limit theorem
- Generalized distributions
- Compound Poisson distributions
- Mixed distributiuons
- Tail behavior based on frequency or severity tail
- Log concavity properties
- Pricing small insurance portfolios on a claim by claim basis
- Analysis of default probabilities
- Allocation of capital and risk charges
- Detailed creation of marginal loss distributions that can then be sampled and used by other simulation software, e.g. to incorporate dependence structures, or in situations where it is necessary to track individual events, e.g. to compute gross, ceded and net bi- and trivariate distributions.
Here are some important things that aggregate does not do:
- It is strictly univariate. It is impossible to model bivariate or multivariate distributions. As a result aggregate is fast and accurate
- aggregate can model correlation between variables using shared mixing variables. This is adequate to build realistic distributions but would not be adequate for an industrial- strength insurance company model.
Where to get it
- The source code is currently hosted on GitHub at:
pip install aggregate
Contributing to aggregate
All contributions, bug reports, bug fixes, documentation improvements, enhancements and ideas are welcome.
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