Numerical Issues

Discretizing Severity Distributions

• Bucket shift (vs. more complex methdods - KPW/LDA) - not a big deal

• Sum to 1 (to normalize or not to normalize?) huge issue: can’t cumsum for levs; convol messes up

• Left tail right tail S vs F computation of diffs

• Cum sum as approx to ?Simpson half h rule integrals

Example (Bahnemann Ch 6 LEV calc)

a = build('agg B.Ex.6.3 1 claim '
          'sev exp(7) * lognorm 2.4 '
          'fixed', bs=50, log2=17, normalize=False,
        discretization_calc='survival')

Try computing the LEVs (match exact calc is easy) with sigma = 2.4 or 0.24 to same range Look at actual S, F and see if they sum as expected.

Does sev_density and agg_density match expected?

The issues are in aggregate.density_df property (but flow through to the portfolio in add_exa).

posted 2022-10-23 | tags: Actuarial exams, aggregate, compound distribution, insurance modeling