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.

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