 # Loss Tools

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### Description by Example

Example 1: Basic FFT Computations
Compute the FFT or IFFT of an user-input vector.
Example 2: Moment Estimator
Compute the mean, CV and skewness of the frequency and severity components of an aggregate distribution, and of the aggregate itself.
Example 3: Step-by-Step Convolution: Inputs
Compute the distribution of the sum of two random variable using FFT methods. Each step of the computation is clearly spelt out.
Example 4: Computing Frequency Distributions
Compute frequency distributions as an aggregate distribution with degenerage severity component using FFT techniques.
Example 5: Create an Aggregate Distribution from a User Input Severity Distribution
Apply a frequency distribution characteristic function to the FFT of a user input severity distribution to compute an aggregate distribtuion.
Example 6: Create an Aggregate Distribution from Cat Model Output
Apply a frequency distribution characteristic function to the FFT of a user input density or sample to compute an aggregate distribtuion. The AIR cat model produces samples; RMS produces densities. Output from either model can be cut and pasted into this example.
Example 7: Create a General Aggregate Distribution
Select from Poisson, Negative Binomial and Poisson-Inverse Gaussian frequency distributions and a wide range of severity distribution, and select layer and attachment of severity distribution to compute an aggregate distribution.
Example 8: Model a Portfolio of Risks
Combine aggregates, specified as in Example 7, to model a portfolio of risks. Compare aggregates made with different assumptions.
Example 9: Triangles and Bootstrapping
Apply boostrap re-sampling to loss development factors to compute a distribution for factors-to-ultimate (FTU). Combine with traditional link ratio methods to determine approximate confidence intervals for ultimate losses.
Example 10: Simple Bivariate Distribution Examples
Model dependence using copulas. Determine two dimensional aggregate distributions using FFT methods.
Example 11: Copulas and Full-featured Bivariate Distribution Examples
Extends Example 10, allowing the user to define a bivariate distribution with per occurrence limits, an aggregate frequency distribution with possible depence between the components (such as loss and ALAE), and then apply aggregate reinsurance. Also models the distribution of (X, X+Y) for input X and Y (incurred loss and IBNR).
Example 12: Mixtures and Assessing Model Fit vs. Large Loss Experience
Compare empirical and theoretical models for large loss experience. Produces comparisons of the density, distribution and survival functions, the mean excess values, and a quantile-quantile (QQ) plot.
Example 13: Loss and ALAE in Excess Reinsurance Layers
Compare the distributions of ceded loss when ALAE is included vs. pro rata in-addition. Compare result of modeling correlation using a copula with simply adding white noise.
Example 14: Bootstrap and Revision of Ultimates
Given a loss development triangle and prior distribution for ultimate losses, compute the posterior distribution, using a combination of bootstrap and Bayesian methods. Extends Example 9 to the full distribution of ultimate losses. This example also demonstrates that Bornhuetter-Ferguson estimates are Bühlmann credibility estimates!
Example 15: Claim Count Development Model
A probabilistic, individual claim-based model for creating claim development factors-to-ultimate.
Example 16: Iman-Conover Method for Inducing Rank Correlation in Marginal Distributions
The Iman-Conover method will induce a specified rank correlation in given marginal distributions by shuffling the marginals. Positive correlation corresponds to shuffling larger values with other larger values; negative correlation corresponds to matching larger values with smaller values.
Example 17: Closed Claim Factor-To-Ultimate Model
An extension of Example 15 to the case of closed claims with no partial payments. CWOPs can be included.
Manual of MALT Functions
Description of all MALT functions.
Ideas for Further Development
Appendix: Built-In Curve Parameters
Displays the curves in the built in parameter file. Explains how to make your own parameter file and how to change the default parameter file.

### Examples by Topic

 Basic FFT Methods Example 1, Example 3, Example 4, Example 5 Computing Aggregate Distributions Example 5, Example 6, Example 7 Combining Aggregate Distributions into a Portfolio Example 2, Example 8 Loss Development, Boostrap, Bayesian Techniques Example 9, Example 14, Example 15, Example 17 Model Fit Example 12 Bivariate Distributions Example 10, Example 11, Example 13, Example 14, Example 16 Loss and ALAE Example 13