# 📋 Settlement Ratio Gap

Why does a 98% CSR become 88% — for the same insurer, same year?

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The Problem

Claim Settlement Ratio (CSR) is the single number consumers use to pick a life insurer. Most headlines report it by claim count . But for anyone holding a large policy, the number that actually matters is CSR by claim value — and the two are rarely the same.

This project asks: is that gap random noise, or something structural?

## 💡 Two Findings That Changed the Frame

① The gap is not a coincidence

Out of 117 insurer-year observations, 115 showed a negative gap — amount CSR below count CSR. p = 8.31 × 10⁻³²

This isn't a reporting artifact. It's a mathematical consequence of how claims get investigated.

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② The same data, two completely different rankings

                  by Count          by Value        Shift
  HDFC Life       98.52%  (#3)  →   88.52%  (#20)   ↓ 17 ranks
  Aegon           97.68%  (#6)  →   96.24%  (#4)    ↑  2 ranks
  Shriram         89.62%  (#18) →   77.30%  (#24)   ↓  6 ranks

A policyholder choosing HDFC based on its "99% CSR" headline is reading a number built from small-claim experience — not theirs.

## ⚙️ The Mechanism

The gap has an exact identity — no distribution assumptions required:

$$ \text{Gap} = \frac{\text{Cov}(X,; p(X))}{\mathbb{E}[X]} $$

As long as larger claims face more scrutiny (p'(x) < 0), the covariance is negative, and the gap is mathematically unavoidable .

This project also introduces Investigation Intensity — a behavioral metric that captures how differently an insurer treats small vs. high-value claims:

$$ \text{Investigation Intensity} = -\text{Gap} \times \mathbb{E}[X] $$

It re-ranks insurers in ways CSR alone never could.

## ⚖️ Honest Trade-offs

✅ Solid	⚠️ Caveat
Gap identity is mathematically exact	β̂ estimates assume uniform CV = 1.5
98.3% sign test is near-certain	Gap ≠ proof of intentional claim rejection
Investigation Intensity proxy is valid	Individual death claims only — no group/health

## 🗺️ What's Next

• Fit logistic regression on individual claim records to validate β̂ directly
• Segment by product line — does β differ for term life vs. ULIP?
• Extend to other regulators
• Consumer tool: "Enter your sum assured → find the right insurer for your risk profile"

## 📁 Repository

├── notebooks/
│   └── claim_decision_model.ipynb          ← Monte Carlo: lognormal · Pareto · Weibull
└── outputs/
    └── working_paper.pdf                   ← full working paper (LaTeX)

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*"Settlement Ratio Gap is not just a reporting number —* *it's a window into how a company's claim decision engine actually works."*
**Kristianto** · Insurance & Risk Analytics · [kristianto.pages.dev](https://kristianto.pages.dev/) · March 2026