Non-life insurance mathematics

1. Non-lifeinsurancemathematics Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring

2. PhD in risk analysis, Institute for Mathematics, University of Oslo 11 yearsexperience from insurance • Senior Actuary in DNB Skadeforsikring (currentposition) • Actuary in Gjensidige • Actuary in KLP • Actuarialconsultant in Avenir 6 yearsexperience from othersectors (energy, research) • Quantitativeeconomic risk assessments (consulting, research) 2 yearspre-graduateexperience (teamleader/instructor in military, transport) MemberofNorwegianActuarial Association nilsfri@math.uio.no Aboutthelecturer

3. Overviewofthissession Module Contents Part in EB* Basic concepts • Intro • Pricing • Portfolio and solvency • Risk ceding and reinsurance • Result elements with risk drivers • Risk selection and pricing • 1.2.1 • 1.2.2 • 1.2.3 • 1.2.4 General insurance: an openinglook • Intro • Enter contracts and theirclauses • Stochasitcmodelling • Risk diversification • 3.2.1 • 3.2.2 • 3.2.3 • 3.2.4 • Howarerandom variables samled? • Inversion • Introduction • Computingthe reserve • Whenresponsibility is limited • Dealingwithreinsurance • 2.3.1 • 2.3.2 • 3.3.1 • 3.3.4 • 3.3.5 • 3.3.6 How Monte Carlo simulation is put to work Someimportantconceptsof real life (if time) • Loss ratio • Costs • Combined ratio EB*=Computation and modeling in insurance and finance by Erik Bølviken

4. Overview Non-lifeinsurance from a financialperspective: for a premium an insurancecompanycommitsitself to pay a sum if an event has occured Contractperiod, a year in propertyinsurance Result elements retrospective prospective The balancesheet Policy holder signs up for an insurance Premium Income Policy holder payspremium. Insurance company starts to earnpremium Losses Loss ratio During thedurationofthe policy, someof thepremium is earned, some is unearned • How muchpremium is earned? • How muchpremium is unearned? • Is thepremiumsufficient to cover incurred (retrospective) and future losses (prospective)? Costs

5. Whydoes it work?? Client 1 Client 2 Result elements Insurance company The balancesheet Client n-1 Client n Premium Income Losses • Economic risk is transferred from the policyholder to theinsurer • Due to thelawoflargenumbers (manyalmostindependentclients), the loss oftheinsurancecompany is much more predictablethanthatof an individual • Thereforethepremiumshould be basedontheexpected loss that • is transferred from the policyholder to theinsurer Loss ratio Costs Muchofthecourse is aboutcomputingthisexpected loss ...but first someinsuranceeconomics

6. How cantheresultof an insurancecompany be decomposed? Result elements Insurance economics in its most basic form: The balancesheet Premium Income Losses Loss ratio Costs

7. Insurance mathematics is fundamental in insuranceeconomics The result drivers ofinsuranceeconomics: Result elements The balancesheet Premium Income Losses Loss ratio Costs

8. Insurance economics • Risk selection: Object risk Result elements The balancesheet Premium Income Losses Loss ratio Costs ……whichhouse is most likely to burndown??

9. Insurance economics • Risk selection: subject risk Result elements The balancesheet Premium Income Losses Loss ratio Costs ………..”sloppy” clientwho is alwaysunlucky….

10. Different price elements have different risk drivers Subject Object Geography • Standard • Electrical system • Pipes • Roof • Construction material • The numberofwetrooms and thenumberofkitchens • Buildingyear • Maintenancelevel in general • Electrical system reviewed? • Weather • Climate • Populationdensity • Infrastructurecomplexity • Natural catastrophies • Demography • Policy holder • Age • Profession • Risk aversion • Personality – structured or carefree? • The numberofinhabitants in building • Use • Inhabited by owner • Rental • Vacationuse (inherited?)

11. Findriskodrivers for everyprice element Objekt Insurance object Element • Fire • Water • Cumule • Elektrical system • Construction material • Flood risk • Pipe quality • Weather Risk driver B A C

12. Loss ratio • Shows howmuchofthepremiumincome is spent to cover losses Result elements The balancesheet Premium Income Losses Loss ratio Costs • Whatdoesthedifference in loss ratio gross and net tell us?

13. Loss ratio • The graph presents loss ratio for all insurancecompanies for villa, content and cabin • The graphillustratesthedelay in thepriceadjustments and theneed for reinsurance • The graphillustratestheeffectofclaimsfrequency (frost 2010) • Source: FNO.no • Differenceof 33 pp in 6 years !?! • Yearlypremiumof 9 billion Loss ratio villa, content and cabin 1998-2011 Result elements The balancesheet Premium Income Losses Loss ratio% Loss ratio Costs

14. Costs Result elements The balancesheet • Sales costs: Provisions, sales offices, marketing, back-office sale • Insurance relatedoperationcosts: management, accounting, actuary, house rent, HR, IT etc.Up to 2012 alsoclaimssettlingcosts– NB:theseweretransferred to claims in 2012 • Receivedprovisionreinsurance: - Normally it constitutes 20% to 25% ofcededpremium.. - NB: ”Costincome” in thetable – why? • - Why do thecompaniesreceivethisprovision? Premium Income Losses Loss ratio Costs

15. Cost ratio (percent) • Shows howmuchofthepremiumincome is spent to cover operationalcosts Result elements The balancesheet Premium Income Losses Loss ratio Costs • Whatdoesthedifference in cost ratio gross and net tell?

16. Cost ratio (percent) Cost ratio Result elements The balancesheet Premium Income Losses Loss ratio • What is causingthereduction in cost ratio to 20%?Where arethecompanies heading? • Source: fno.no– Results in non-lifeinsurance: includes all non-lifeinsurancecompanies in Norway Costs

17. Combined ratio • Shows howmuchofthepremiumincomethat is spent to cover claims and operationalcosts Result elements The balancesheet Premium Income Losses • Combined ratio above100 % impliesthattheinsuranceoperationsare not profitable • What do thecombined ratio gross and netexpress for theexamplecompany? • Long term CR for insurancecompanies in Norwayarebetween 90% and 95% • Whatkey ratio is most problematic for theexamplecompany? Loss ratio Costs

18. Key parameters for non-lifeinsurance in Norway • The graph shows loss ratio (leftaxis), resultdegree (total revenue minus total costs, right axis), cost ratio (right axis) andincome from investments in percentofpremium (right axis) for theperiod1998-2011 • The resultdegree and the loss ratio vary a lot. • The loss ratio seems to be the most important driver for profitability in non-lifeinsurance • The cost ratio and income from investments in percentofpremiumaredecreasing during theperiod. Result elements The balancesheet Premium Income Loss ratio Losses Resultdegree Loss ratio Cost ratio Income from investments as percentofpremium Costs

19. Outlineofthecourse

20. Course literature Curriculum: Chapter 1.2, 2.3.1, 2.3.2, 2.5, 3.2, 3.3 in EB Chapter 8,9,10 in EB Note onChain Ladder Lecture notes by NFH The following bookwill be used (EB): Computation and Modelling in Insurance and Finance, Erik Bølviken, Cambridge University Press (2013) • Additions to the list abovemayoccur during thecourse • Final curriculum will be postedonthecourse web site in due time