Lecture 18 - Capital Shocks Apr 7

Lecture 18 - Capital Shocks Apr 7 - Insurance Company...

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Unformatted text preview: Insurance Company Capital Insurance Company Capital • An insurance firm sells 1,000 policies to consumers with independent and identical risk exposures. Each consumer faces a 1 percent chance of a $2000 loss. • Assume the firm has no selling expenses, and assume no discounting or profit loading. • The insurer wants to maintain a probability of insolvency less than 0.1 percent and has $15,000 initial capital. • What is the minimum the insurer can charge per policy? Distribution of X Distribution of X X E(X) Funds needed per policy Area under curve = 0.1 percent Solution Solution • E(loss) = $20; Var(loss) = $39,600 • Var(average loss) = $39,600/1000 = 39.6 • S.D.(average loss) = (39.6) 1/2 = 6.29 • Funds needed per policy: 20 + 3(6.29) = $38.88 • Funds available per policy (from capital): $15,000/1000 = $15 • Minimum premium to meet target insolvency probability: $38.88 - $15 = $23.88 • Total funds needed (capital + premiums) for 1,000 policies: $38,880 Insurance Company Capital Insurance Company Capital Suppose that the insurer cedes 20 percent of all losses to a reinsurer. A proportional reinsurance treaty: The reinsurer pays 20 percent of losses The reinsurer gets 20 percent of premiums The insurer wants to maintain a probability of insolvency less...
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This note was uploaded on 05/07/2009 for the course PAM 4230 taught by Professor Tennyson during the Spring '07 term at Cornell.

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Lecture 18 - Capital Shocks Apr 7 - Insurance Company...

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