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Math 479/568

Casualty Actuarial Mathematics

Fall 2014University of Illinois at Urbana-Champaign

Professor Rick Gorvett

Session 12: Reinsurance I

October 9, 2014

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Agenda

• Reinsurance I

– Basic concept

– Who’s responsible for the loss?

– Purposes and functions

– Types

– Issues

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Reinsurance – the Basic Concept

• “Reinsurance” is essentially the “insurance of insurance”– One insurer “shares” its business with another– Both the premiums and losses are shared– Sharing can occur as a percentage, or based on a

size-interval of loss

Reinsured

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The Basic Concept (cont.)

• Framework:– Insurer sells an insurance policy to the insured– Insurer (possibly) purchases reinsurance from

reinsurer(s)• Could be automatic (i.e., applies to the policy as part

of a broad reinsured group)• Could pertain to just that policy

– Insured is not involved in the reinsurance transaction, and may not even be aware that reinsurance applies to her/his risk

– “Retrocession”: a reinsurance transaction on already reinsured risks

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“Layers” of Responsibility

• Policyholder (or insured)– Responsible for losses within the deductible– Responsible for losses above the policy limit– Also responsible for any “copayment”

• Insurer (or “ceding company”)– Collects premiums and pays losses according to the

policy provisions– May cede some premium and loss to reinsurer(s)

• Reinsurer(s)– Reimburses insurer for reinsured payments

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Purposes and Functions of Reinsurance

• Catastrophe protection / limitation of liability– Possible bases of catastrophic limit application

(from perspective of ceding company):• Maximum payable on an individual risk

• Maximum payable for an individual event

• Maximum payable in the aggregate (e.g., per year)

– Reduces impact of significant events

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Purposes and Functions of Reinsurance (cont.)

• Stabilization– Reduces variability of insurer results by “smoothing out” loss experience• E.g., in catastrophe reinsurance, large loss peaks are

reinsured – for a price

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Purposes and Functions of Reinsurance (cont.)

• Capacity– Insurer can take on more risk – e.g., write higher

policy limits

• Financial management– Timing of certain accounting / cash flow items

can be altered and managed

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Types of Reinsurance

• Treaty versus facultative– Treaty: a contract by which underlying insurance

policies of a specified type are each subject to a reinsurance program

– Facultative: reinsurance parameters (and whether reinsurance applies at all) are individually decided / negotiated for each underlying insurance policy

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Types of Reinsurance (cont.)

• Proportional (or “pro rata”) versus Excess– Proportional

• Quota share – percentage sharing of business• Surplus share

– Excess• Per Occurrence – for each loss, the reinsurer

pays that portion of the loss above a certain dollar threshold (the ceding company’s “retention”)

• Per risk• Aggregate

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Issues

• Leveraged effect of inflation– Over time, more claims will trend, or inflate, into

an excess reinsurance layer– Claims that are already above the retention will

be further above the retention after inflation, with all of the additional cost of the claim going to the excess layer

• Collectibility of reinsurance

• Pricing of reinsurance– Time value of money is critical

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More Issues

• Ceding commissions

• Treatment of allocated loss adjustment expenses

• Quantities and terminology– Gross versus net– Subject premium

– “Inures to the benefit of”

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2008 CAS Exam 6, Problem # 26

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2008 CAS Exam 6, Problem # 28

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2008 CAS Exam 6, Problem # 29

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2008 CAS Exam 6, Problem # 32

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2008 CAS Exam 6, Problem # 33