Gift Re Pricing Lab

Ground-up severity: real vs synthetic

Real eventsWGAN-GPWGAN-GP + EVT tail

Annual cedant loss to the layer

Ground-up annual loss (cedant share)

Layer loss by return period

Technical premium by method

Build-up (selected method)

Mean-excess plot (real data)

A roughly linear, upward-sloping mean-excess function above the chosen threshold u supports a GPD tail with ξ > 0. The vertical marker is the fitted threshold.

Threshold stability of ξ

The MLE of ξ should be roughly flat across thresholds above a valid u (Pickands–Balkema–de Haan).

Critic Wasserstein estimate during training

WGAN-GP with a one-sided Lipschitz penalty (λ = 10, n_critic = 5, Adam 1e-4). The critic's estimate of W(P_r, P_g) shrinking towards zero indicates the generator distribution approaching the data.

Fidelity vs the traditional benchmark

Real events used for this peril

Trending to 2024 exposure

Nominal losses are deflated with India CPI (World Bank) to 2024 prices, then scaled by (real GDP₂₀₂₄ / real GDP_t)^0.5. The 0.5 elasticity is a compromise between pure inflation adjustment and full Pielke-style normalisation, reflecting improved flood defences and building codes. USD figures are converted at year-average USD/INR.

Cedant loss = economic loss × insured share × market share for the loss-based perils. The drought peril is parametric: the payout is a function of the rainfall-deficit index and needs no claims data.

Public data catalogue for India

1 · DataCWC flood damages 1953–2016, India cyclone event losses 1972–2025, USGS catalogue + earthquake loss table, IMD sub-division rainfall 1901–2015. Trended to 2024.

2 · Conditional WGAN-GPGenerator G(z | c) with c = monsoon departure / wind speed / magnitude. Learns the body of the severity distribution (and, for drought, the 21-dimensional spatial correlation of deficits).

3 · EVT spliceGPD fitted to real excesses over u by MLE (profile MLE with an analogue ξ when data are too thin). Every synthetic value above u is replaced by u + GPD excess.

4 · FrequencyPoisson event counts from the observed rate (cyclone landfalls with loss since 1990; shallow M ≥ 6 events since 1960). Annual perils use one draw per year.

5 · Layer & capitalRecovery = min(max(L − A, 0), Lim), aggregate cap Lim × (1 + reinstatements). Capital = TVaR_99.5 − E[L]. Premium = E[L] + expenses + CoC × capital − float credit.

W(P_r, P_g) = sup_{‖D‖_L ≤ 1} E_{x~P_r}[D(x)] − E_{x̃~P_g}[D(x̃)] L_D = E[D(G(z|c))] − E[D(x|c)] + λ · E[ max(0, ‖∇_x̂ D(x̂)‖₂ − 1)² ] (one-sided Lipschitz penalty) F_u(y) = P(X − u ≤ y | X > u) ≈ 1 − (1 + ξ y / σ)^(−1/ξ) (Pickands–Balkema–de Haan) VaR_α = u + (σ/ξ) · [ ((1 − α)/P(X > u))^(−ξ) − 1 ] TVaR_α = (VaR_α + σ − ξ u) / (1 − ξ) Technical premium = E[L] + e·E[L] + r_CoC · (TVaR_99.5 − E[L]) − f·E[L] Rate on line = Premium / Limit

Governance controls implemented

EVT is fitted on real excesses, never on the generator's own output, so the tail cannot be self-referential.
Every peril is priced side-by-side with a lognormal MLE fit and an empirical bootstrap; large divergence is a signal for actuarial review, not a result.
Synthetic scenarios are a supplement: the generator is seeded on Indian data plus physical hazard covariates; new-line exposure should be capped until real experience accumulates.
Reporting: KS and Wasserstein-1 distance to the real sample, ξ bootstrap interval, hold-out backtest (flood 2017–21).