Insurance Claims Padding — Probabilities & Risk-Management
Scenario
An estimated 45% of U.S. adults will try to pad their insurance claims to cover a deductible. An insurance adjustment office has received n = 120 claims to process. Let X be the number of claims padded. Assume X ~ Binomial(n=120, p=0.45).
Probability Results (rounded to 4 decimal places)
| Event | Probability (exact) | Rounded (4 d.p.) |
| A. Half or more of claims padded: P(X ≥ 60) | 0.156443 | 0.1564 |
| B. Fewer than 45 claims padded: P(X ≤ 44) | 0.039877 | 0.0399 |
| C. From 40 to 64 padded: P(40 ≤ X ≤ 64) | 0.969147 | 0.9691 |
| D. More than 80 not padded (i.e. padded < 40): P(X ≤ 39) | 0.003553 | 0.0036 |
Interpretation — What the Numbers Mean
Event A (P = 0.1564): There is about a 15.64% chance that half or more of the 120 claims will be padded. This is a moderate probability and suggests the office should be prepared for such an outcome.
Event B (P = 0.0399): There is only about a 3.99% chance that fewer than 45 claims are padded — a relatively unlikely low-fraud scenario.
Event C (P = 0.9691): There is a very high probability (~96.91%) that the number of padded claims will fall between 40 and 64; this is the most likely outcome band and can be used for routine staffing and triage planning.
Event D (P = 0.0036): There is a tiny chance (~0.36%) that more than 80 claims are NOT padded (equivalently padded < 40). This low probability indicates the office need not plan primarily for unusually low padding levels.
Risk-Management Recommendations for an Adjustment Office
1) Staffing & Triage
Use the most likely outcome band (40–64 padded claims) to plan staffing levels and expected workload for fraud handling. Schedule peak examiner capacity accordingly and prepare a small surge team for the ~15.6% chance of ≥60 padded claims.
Adopt a triage system that routes higher-risk claims to experienced adjusters and lower-risk claims to faster processing queues. Criteria for triage can include claim amount, claimant history, and anomaly scores from automated checks.
2) Detection & Audit Sampling
Given the possibility of significant padding, run pre-screening analytics (outlier detection, text mining of descriptions, frequency of small repairs near deductible thresholds).
Implement targeted audit sampling: for example, audit a random sample PLUS a focused sample of borderline claims near the deductible, to estimate realized fraud rates and adjust p estimates.
3) Reserves & Financial Controls
Use expected-case projections (e.g., expect ~54 padded claims on average since E[X]=n·p=120·0.45=54) when estimating short-term processing reserves and potential recovery efforts.
Maintain a contingency reserve or reinsurance arrangement for the ~15% chance of heavier-than-expected padding (≥60).
4) Prevention & Claims Design
Reduce incentives to pad claims by reviewing deductible levels, simplifying claims for small loss amounts, and speeding payments for legitimate small claims to discourage padding.
Consider offering no-deductible options for certain low-frequency customers or increasing thresholds for required documentation for small claims.
5) Analytics & Feedback Loop
Continuously update the estimate of p using observed data; re-run binomial projections regularly (monthly/quarterly) to detect changes in behavior or seasonal effects.
Feed outcomes back to the underwriting team: adjust pricing, deductible structures, or customer education if padding rates change materially.
6) Legal, Ethical & Customer Communication
Ensure anti-fraud policies are communicated clearly and enforced fairly. Balance fraud control with excellent customer service to avoid alienating honest claimants.
Train staff in fair investigation techniques and maintain careful documentation for any recoveries or denials.
Note in the day and age of social media insurance companies are in an awkward position of reputational risk. If they fail to pay the reputational risk is that they are to hard, pay to much or to readily the reputation is they are a claims pushover. So, it is a matter of managing fraud, reputation (good and bad) and the associated PR.
risk management extends beyond the math.
Numeric Summary
Expected number padded (mean): E[X] = n·p = 54.00 (≈ 54)
Event probabilities (rounded): A = 0.1564 (15.64%), B = 0.0399, C = 0.9691, D = 0.0036
