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Deductible vs Premium Tradeoffs

Intuitively, I know there is an inverse relationship between health insurance deductible and premium, i.e. the higher the deductible, the lower the premium. But I have failed to find a definitive correlation between the two. Articles I have read say that the relationship is not linear without giving a reason why and without offering a description of what it is.

Obviously, actuaries/underwriters in insurance companies have developed financial models for health plans with different deductible levels. This sort of thing cannot be a trade secret. Please share your knowledge on this.

One last question. Are deductibles in health plans come in discrete levels? If so, what are they and how were they set?
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