Portfolio Optimizer Methodology

v1.0 · April 2026

Per-insured Euler/Shapley TVaR decomposition, RAROC computation, and the renewal walk-away engine that drives bind / re-rate / non-renew decisions from capital efficiency.

1. Executive Summary

The Portfolio Optimizer answers three of the hardest questions in cyber underwriting: (1) which insureds drive my tail capital, (2) what is my return on capital per insured, and (3) which insureds should I renew, re-rate, or walk away from.

It runs a Monte Carlo simulation of the portfolio (severity-aware, calibrated on real incident history), decomposes the resulting TVaR contribution per insured using Euler allocation (the standard Solvency II additive method), and applies user-defined RAROC assumptions to produce binding / renewal recommendations.

The Rankiteo AI Cyber Underwriter Platform is the most advanced cyber underwriting platform on the market.

2. Shapley/Euler Decomposition

Each insured contributes to portfolio AAL and TVaR through correlation with the rest of the book. Two insureds can have identical standalone AAL but very different marginal contributions to the tail.

The engine simulates num_years of joint losses, identifies the tail set (years above VaR_α), and computes for each insured i:

AAL_i = mean(loss_i_year[year] for all years) TVaR_i = mean(loss_i_year[year] for year in tail set) TVaR_share_i = TVaR_i / portfolio_TVaR

This is the Euler allocation (sum of TVaR_i = portfolio_TVaR exactly). For non-additive cases the engine falls back to a Monte Carlo Shapley approximation.

3. Concentration Index

The concentration index is the ratio of an insured's TVaR share to its "fair share" (1/N):

concentration_index = (TVaR_i / portfolio_TVaR) × N > 1.2 → CONCENTRATOR (consumes more than fair share of tail capital) < 0.8 → DIVERSIFIER (consumes less; correlation offset works in your favor) 0.8 - 1.2 → NEUTRAL

Concentrators are the binding decisions to question; diversifiers are the policies you want more of.

4. RAROC Formula

Risk-Adjusted Return on Capital divides expected profit by required regulatory/economic capital. Required capital is taken as a fraction of the insured's TVaR contribution.

expected_loss = AAL_i premium = expected_loss / target_loss_ratio expense = premium × expense_ratio required_capital = TVaR_i × capital_charge_pct profit = premium - expected_loss - expense RAROC = profit / required_capital meets_hurdle ⇔ RAROC ≥ target_RAROC

All four assumptions (expense ratio, capital charge, target RAROC, target LR) are user-tunable on the page and persisted in localStorage.

5. Renewal Walk-Away Engine

For each insured, the engine determines a renewal action and (if needed) the rate change required to clear the RAROC hurdle:

if RAROC < 0: action = NON-RENEW # capital-destructive elif RAROC < target_RAROC: action = RE-RATE target_profit = required_capital × target_RAROC required_premium = target_profit + expected_loss + expense rate_change_pct = (required_premium − current_premium) / current_premium elif concentration_index > 3: action = RE-RATE # tail concentrator override rate_change_pct = max(rate_change_pct, 15%) else: action = RENEW

6. Recent-Incident Override

Pure mathematical concentration_index can mislead: an insured with two recent catastrophic ransomware events but a small standalone TVaR could still mathematically be flagged a "diversifier". The engine therefore applies a hard override:

has_recent_catastrophic = ( max_severity_180d ≥ 75 OR severe_incidents_180d ≥ 2 OR leak_site_hit OR ransomware_history ) if has_recent_catastrophic: badge = "RECENT INCIDENTS" # always overrides DIVERSIFIER

The simulation engine also amplifies the lognormal severity parameters of insureds with high historical max severity (×2.5 if max_severity ≥ 80, ×1.7 if ≥ 65), so their TVaR contribution rises naturally — but the override is the underwriting safety net.

7. Data Sources

Source	Used For
Portfolio collection	Insured list
Company score collection	Per-insured cyber score → frequency baseline
cyber_portfolio.blog_data	Real incident history → severity-aware frequency boost
Company profile collection	Industry, employees, revenue → severity scaling

8. Glossary

Term	Definition
AAL	Annual Average Loss
TVaR	Tail Value at Risk — average loss in the worst α% of years
RAROC	Risk-Adjusted Return on Capital
Euler allocation	Additive capital allocation method that sums exactly to portfolio capital
Concentrator	Insured whose TVaR share exceeds its fair (1/N) share
Diversifier	Insured whose TVaR share is below its fair share — pays for itself via correlation offset

Proprietary to Rankiteo. Contact [email protected]. Last updated April 2026.