Mildenhall Aggregate

Loss Tools

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Ideas for Future Development

Class	Methods
AggCo	Construct a BivEmpCo density from a bivariate sample Constants for scripting, like OWC
FinCo	Pricing finite reinsurance: combine with the Portfolio class; allow user to input payout patterns by line of business, contract terms etc. Return pricing statistics for various finite reinsurance structures.
ParamFile	Add suggested contagion factor
Portfolio	.Stats method: return all stats, TLN fits and estimated unit, for each member of the portfolio and for the aggregate. Return density, using common input unit Multivariate sample: sort out code. Some kind of persistence implementation.
EmpCo	InverseDist: compute the distribution of 1/X. Returns a new EmpCo.

Other Issues and Research Ideas

Wang review discussion points:
- Summary: MM good for larger claim counts, but use three moments (Example 7 ); FFT very good for small claim counts (e.g. XOL reinsurance); FFT and copulas works well for 2-d distributions with correlation
- Shifted lognormal and shifted gamma distributions; fitting formulae; three moments of aggregate
- For large claim counts and moderate severity distributions, the frequency distribution determines the aggregate.
- Difference between contagion and variance multiplier views of frequency variance for large claim counts.
- Use of two dimensional FFTs and copulas to compute the sum with a given dependency structure.
- Correlation is not enough to specify dependence
- Independent plus noise instead of computing explicitly
- Computing net/gross ceded distributions
- Computing distribution of (X, X+Y)
- LR and results correlation driven through premium correlation, more than loss correlation
- Iman Conover method
- Simulation vs. numerical integration
Correlation
- Correlation is very tricky! Correlation coefficient and marginals do not determine a bivariate distribution (see Iman-Conover example).
- Vitale's Theorem and Iman-Conover
- Simulating from a bivariate distribution by flattening the bivariate distribution. Is there a way to generate points without knowning ahead of time how many you will need (analogous to the Monte Carol sequences)?
Bayesian approach to estimating contagion from historical exposures and observed frequencies.
LDF and CCDF methodology: Bayesian bootstrap method; BF method as Buhlmann credibility; claim count development method; loss development method; practical modeling
Software implementation of very large 2-d FFTs. What is the practical upper limit on size? (Ans: 4096 x 4096 on a standard PC, 128MB memory required.)