Lecture 18 - Capital Shocks Apr 7

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

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This note was uploaded on 05/07/2009 for the course PAM 4230 taught by Professor Tennyson during the Spring '07 term at Cornell.

### Page1 / 17

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online