treaties Conference R in Insurance 29062015 Indra LOLJEEH Technical Advisor Analytics at QBE Re liqberecom Agenda Reminder about reinsurance treaties ID: 524976
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Slide1
Pricing of MAXL treaties
Conference
R in
Insurance
– 29/06/2015
Indra LOLJEEH –
Technical
Advisor
Analytics
at QBE
Re
– li@qbere.comSlide2
Agenda
Reminder
about
reinsurance
treaties
MAXL
treaties
Pricing of MAXL
treaties
Structure of the pricing program
ConclusionSlide3
Agenda
Reminder
about
reinsurance
treaties
Reinsurance
basic
treaties
Aggregate
clauses in
reinsurance
MAXL
treaties
Pricing of MAXL
treaties
Structure of the pricing
program
ConclusionSlide4
Traditional reinsuranceSlide5
Quota-Share
Cession rate:
for all risks
Slide6
Surplus
Cession rate:
for all risks
where
is called the surplus line
Slide7
Excess of loss
Notation: C
xs
D
original claim
amount
Slide8
Stop loss
Notation: C
xs
D
Slide9
Aggregate clauses in reinsurance
AAD:
Ag
gr
egate
Annual
Deductible
AAL: Aggregate Annual LimitLink with Stop-Loss treaties These elements are the basis of most
currently
existing reinsurance structuresSlide10
Agenda
Reminder
about
reinsurance
treaties
MAXL
treaties
Concept of MAXL treaties
Illustration/ExamplePricing of MAXL treatiesStructure of the pricing programConclusionSlide11
Concept of MAXL treaties
Multiline
:
Reinsurance
treaty
covering
several lines of business at the same timeCommon protection for several portfoliosAggregateStructure that contains aggregate clauses (MAAD/MAAL)These clauses are applied on a global leveleXcess of Loss
Non-proportional structureProtection against medium/high claimsSlide12
MAXL ExampleSlide13
MAXL Example
Interior Priority
Eligible Claim ActivitySlide14
Advantages of such structures
Improved
protection
against
medium
sized
claims
Towards
frequencyTowards changes in legislationProtection of insurer’s global resultsCan cover several lines of business at the same timeCheaper than lower XL cover
Optimization of the reinsurance structure (Solvency
II)Slide15
Agenda
Reminder
about
reinsurance
treaties
MAXL
treaties
Pricing of MAXL
treatiesCollective risk model / Monte-Carlo methodsProblems inherent to MAXL treatiesCorrelationsLines of business (ST/LT)TimeWhat R brought
to us Structure
of the pricing programConclusionSlide16
Theory behind the pricing of MAXL
Collective
Risk
model:
Independency
between
frequency
and severityDetermination of the loss distribution of the eligible layersDetermination of the frequency distributionsAggregation of the loss distributionsUse of copulasDependency structure between the lines
of business ?Dependency above thresholds ?
Long tail vs. Short tail businesses ?Use of Monte-Carlo simulationsSimulation for each line of businessAggregation to obtain aggregate
loss distributionSlide17
Problems inherent to such
methods
Time-
consuming
process
Need
for an efficient softwareMany underlying structures possible Need for program flexibilityStill some
developments needed for the copula part
Need for a modular programDifficult to take account of some distributions (CAT Softwares)
Slide18
Problems inherent to such
methods
Time-
consuming
process
Need
for an efficient softwareMany underlying structures possible Need for program flexibilityStill some
developments needed for the copula part
Need for a modular programDifficult to take account of some distributions (CAT Softwares)
R
is
our savior !!!Slide19
Agenda
Reminder
about
reinsurance
treaties
MAXL
treaties
Pricing of MAXL
treatiesStructure of the pricing programConclusionSlide20
Structure of the pricing programSlide21
Global distribution Slide22
Agenda
Reminder
about
reinsurance
treaties
MAXL
treaties
Pricing of MAXL
treatiesStructure of the pricing programConclusionSlide23
Advantages of R in our case
Ideal
for simulation
based
tools
Simplification of the audit
process
Program easy to modify and improvePackages already existingPossibility for further analysis on dataGraphsSensitivity analysisReportingSlide24
Questions?