Lecture Notes 12 - University of Illinois at Urbana

Math 479/568
Casualty Actuarial Mathematics
Fall 2014
University of Illinois at Urbana-Champaign
Professor Rick Gorvett
Session 12: Reinsurance I
October 9, 2014
• Reinsurance I
– Basic concept
– Who’s responsible for the loss?
– Purposes and functions
– Types
– Issues
Reinsurance – the Basic Concept
• “Reinsurance” is essentially the “insurance of
– 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
The Basic Concept (cont.)
• Framework:
– Insurer sells an insurance policy to the insured
– Insurer (possibly) purchases reinsurance from
• 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
“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
Purposes and Functions of
• 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
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
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
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
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
• Per risk
• Aggregate
• 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
More Issues
• Ceding commissions
• Treatment of allocated loss adjustment
• Quantities and terminology
– Gross versus net
– Subject premium
– “Inures to the benefit of”
2008 CAS Exam 6, Problem # 26
2008 CAS Exam 6, Problem # 28
2008 CAS Exam 6, Problem # 29
2008 CAS Exam 6, Problem # 32
2008 CAS Exam 6, Problem # 33

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