The problem

• Desire for individual claim analysis - don’t throw away data.
• We’re all pretty comfortable with GLMs now. Let’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!

More optimistically …

• 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. Let’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.

What I’ll show you

• 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 won’t talk about:

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

Guszcza and Lommele

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.