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Portfolio Risk Adjusted Premiums - Matching PI's Profit Probabilities

Assume that brand new and (actually Claims Costs Managers) want 's probability (0.8413) of earning profits of at least 5% on portfolios of 100,000 (10,000) policyholders. Their standard errors are higher than 's, so = 0.9581 (0.7500 + 0.0500 + 1 * 0.1581) and = 1.3000 (0.7500 + 0.0500 + 1 * 0.5000) are the portions of each dollar of 's Earned Premiums and need to match 's probability of earning profits of at least 5% on their portfolios.If pays 10 s [100 s] less than 95.81% (0.7500 + 0.05 + 15.81) [130.00% (0.7500 + 0.05 + 0.5000)] of its Earned Premiums for transferring its Claims Costs, they do not match 's profit probability. If adequately compensates and , it incurs catastrophic operating losses of 10.81% and 45% on each transfer, becoming insolvent, and about 62.41% of 's will have PLREs below 0.8000, as will 53.98% of 's, so they will be grossly overpaid by 15.81% and 50% of 's Earned Premiums.

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Thomas Cox PhD RN
2013-02-23