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I was searching for a definition of risk sharing and I have found the following:

$\underline{Definition:}$ Risk Sharing — also known as "risk distribution," risk sharing means that the premiums and losses of each member of a group of policyholders are allocated within the group based on a predetermined formula. Risk is considered to be shared if there is no policyholder-specific correlation between premiums paid into a captive, for example, and losses paid from the captive's reserve pool.

I am confused with the term "captive". What is the exact meaning of this term? Is there any other reference about seome definition of risk sharing?

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Captive insurance is an insurance for purpose of insuring the owners of the said insurance. It’s a kind of self-insurance where multiple agents pool their capital together to insure themselves. So the term in that sentence refers to the pool of resources for insurance.

It’s called captive because the modern concept of this kind of insurance was first applied to a company that wanted to create insurance for its subsidiary mines that were referred to as captives and somehow the term catch on.

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