Individual Claims Reserving with Stan

The problem

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
  • Diagnosing a Stan fit

Guszcza and Lommele

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.