Preston McAfee points me to the following interesting article:

The weird world of kidnapping insurance, by Jeff Spross

"A private market for insuring and dealing with kidnappings might sound, at first blush, like a terrible idea. A kidnapping is already a fraught situation; a mix of fear, greed, violence, and coercion that occurs outside the bounds of the law. And private insurers often have a reputation for being cold-blooded and predatory themselves. The average person could be forgiven for balking at the idea of combining the two.

"Yet not only does a private market for insuring kidnappings and advising the negotiations exist — by all accounts it's quite effective. If you're the victim of a kidnapping where professional insurers and negotiators are involved, the chances that you'll come back alive are roughly 97.5 percent.

"The K&R market consists of 20 or so firms, all operating out of Lloyd's of London, an international marketplace based in Britain, where insurance providers, clients, brokers and underwriters can all find one another. The K&R firms compete for business, and provide their clients with both insurance to backstop potential ransom payouts and consultants who help guide and strategize the actual negotiations with the kidnappers. While some wealthy individual families do occasionally buy the services of K&R providers, the vast majority of customers are companies insuring their employees who work in risky areas. Roughly three-fourths of Fortune 500 companies have some sort of policy, with total premiums reaching $250 to $300 million a year.
...
""The only way that kidnapping can work as well as it does is that the kidnappers understand that they're in a repeated business," Anja Shortland, an economist at King's College London, who's written a book on the K&R insurance market, explained to The Week. "They keep their promises this time and they treat the hostages well this time because they know that if they don't then their business will decline in the future."

That's where the private firms who provide the consulting and the insurance coverage come in: "It's a one-off transaction between the family and the kidnapper, but it's a repeated interaction for the insurance market," Shortland said."

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