How the Tax Court’s Risk Distribution Analysis Misapplies the Law of Large Numbers

Sol Feinberg, FCAS, MAAA, Consulting Actuary, and Hale Stewart, JD, LL.M., Attorney

Sol Feinberg and Hale Stewart were recently featured in an article by Captive Insurance Times titled, "How the Tax Court’s Risk Distribution Analysis Misapplies the Law of Large Numbers". In it, they discuss how the US tax court’s approach to risk distribution is rooted in a flawed reliance on the Law of Large Numbers.

The following two paragraphs provide a detailed summary of Captive Insurance Times' overview of the article:

The piece dismantles the IRS’s long-standing “safe harbors”, which arbitrarily require a certain percentage of unrelated premiums (50.01%) or a minimum number of insured entities (12) for tax recognition, despite no actuarial or statistical basis for these thresholds. Through historical and academic evidence, Sol and Hale show that courts and regulators have misapplied the Law of Large Numbers, treating it as a prerequisite for valid insurance when, in fact, it rarely applies cleanly to property and casualty risk.

Sol Feinberg explains, with mathematical precision, why the Law of Large Numbers cannot guarantee stable results for insurers, unlike in casino probability models, because real-world risks are neither independent nor fully known. Instead, insurance viability depends on sound actuarial principles: adequate capital, appropriate pricing, and a regulator’s oversight. Ultimately, the article calls for a reassessment of the legal doctrines governing captives, urging courts and the IRS to ground their reasoning in actuarial science rather than arbitrary metrics. The message is clear: insurance law must realign with insurance reality.

You can read the Captive Insurance Times issue here. Navigate to pages 38-43 to read the full article, "How the Tax Court’s Risk Distribution Analysis Misapplies the Law of Large Numbers".

We welcome discussion with any of our insurance colleagues who want a better understanding of these topics, and those wishing to contact us can do so at support@SIGMAactuary.com or by scheduling a call today with one of our consulting actuaries.

© SIGMA Actuarial Consulting Group, Inc.

Leave a Reply

Your email address will not be published. Required fields are marked *

Archives

Recent Posts

SIGMA's 2025 Highlights
Obstacles and market uncertainty are no strangers to the insurance industry, and 2025 was no different. Despite this uncertainty, our team here at SIGMA persistently directed its focus towards growth, education, and delivering exceptional service to our clients. We were very fortunate to have been r...
Read More
RISK66 - The Path to Strategic Captive Decisions
Al Rhodes was recently featured in an article by Captive Review titled, "RISK66 - The Path to Strategic Captive Decisions". In it, he discusses SIGMA’s RISK66 software and its recent win in Captive Review’s US Awards as “Technology Solution of the Year”, as well as what has made it so unique...
Read More
How the Tax Court’s Risk Distribution Analysis Misapplies the Law of Large Numbers
Sol Feinberg and Hale Stewart were recently featured in an article by Captive Insurance Times titled, "How the Tax Court’s Risk Distribution Analysis Misapplies the Law of Large Numbers". In it, they discuss how the US tax court’s approach to risk distribution is rooted in a flawed reliance on t...
Read More
CPI 101: How the Consumer Price Index Shapes Inflation, Economics, and Actuarial Decisions
The Consumer Price Index (CPI) is a crucial measurement of the cost of living in our economy, and since the economy is always changing, the methods used to calculate the CPI are adapting to that change. In this month's blog, we will be discussing some common questions regarding CPI, such as: what it...
Read More

Subscribe to Our Blog



Copyright © 2023 – 2026 SIGMA Actuarial Consulting Group, Inc. All Rights Reserved.
chevron-down linkedin facebook pinterest youtube rss twitter instagram facebook-blank rss-blank linkedin-blank pinterest youtube twitter instagram