- Desire for individual claim analysis - donâ€™t throw away data.
- Weâ€™re all pretty comfortable with GLMs now. Letâ€™s go crazy with lots of variables.
- Risk management and regulatory oversight mean that second moment estimate becomes more critical
- Mama weer all Bayezee now!

- Actuaries are seen as vital elements in steering the claims department. Must have a laser focus on individual claims.
- Actuaries are our go-to resource for fancy pants predictive models. Letâ€™s use this in our claims department.
- Managers have put up with the limitations of chain-ladder reserving for far too long. We need more technical solutions to old problems.

- Detailed walk through of an example first proposed by Guszcza and Lommele.
- Comment on how this fits with aggregate methods
- Bifurcated data
- Hierarchical models
- Bayesian

- Easy stan walk through
- Stan for individual claims

What I wonâ€™t talk about:

- The stochastic simulation assumptions
- IBNYR
- Diagnosing a Stan fit

Published way back in 2006, Guszcza and Lommele (2006) presented a model to develop reserves based on individual claim data.

- 5,000 claims per year
- Value at first evaluation period is the same, lognormal
- Subsequent amounts are multiplicative chain ladder
- Current period amount equals prior period times link ratio
- Link ratios are random
- Expected value and variance of link ratio depends on credit quality

- Fit the model using a Poisson GLM
- Aggregation of claims data misses the specific structure of the data

Regression based on individual claims looks pretty good. Axes are on a log scale.

However, things look different when we differentiate based on credit grouping.