What method of managing risk involves not purchasing insurance and either paying for all of the loss or a portion through deductibles?

The method of managing risk identified in the question is retention. Retention is a risk management strategy where individuals or organizations choose to bear the financial burden of a loss rather than transferring that risk to an insurance company through the purchase of insurance. This approach often involves the decision to pay for all of the loss outright or to agree to cover a portion of it through deductibles.

In many cases, retention is utilized when the potential losses are relatively small or manageable within a risk-decision framework, and also when the cost of purchasing insurance is deemed greater than the risk of loss itself. By using retention effectively, individuals or businesses can maintain control over their costs while also accepting certain risks as a part of their overall financial strategy.