1. Insurance mathematics I. lecture Introduction References: - Arató Miklós: Általános biztosításmatematika (General insurance mathematics). ELTE, 2000 -George E. Rejda: Principles of Risk Management and Insurance -www.math.bme.hu\~gerenyi Requirement: Elaboration of one task from appointed home works

2. Insurance mathematics I. lecture Basic definitions - Insurance - Policy - Insured - Signatory - Beneficiary - Duration of policy (definite or indefinite) - Premium - Sum insured - Claim payment - Claim event

3. Insurance mathematics I. lecture Basic question -Why do we take out a policy? One possible answer: there are a lot of such risk in our lives which – if it occurs – can cause a financial disruption of our family. For example: - fire regarding our home; - theft from our home; - car crash etc. Insurer can help us to avoid financial collapse.

4. Insurance mathematics I. lecture Example - policy Janos Kis works as a gatekeeper in Cerna manufactory. He is a member of Horgol Insurance Society. The Cerna takes out a disability policy with Horgol at 21.12.2012. The policy contains that if Janos will be disabled in 2013 then Horgol will pay proportional part of 1 million HUF to his wife, Janosne Kis. The premium is 2.500 HUF.

5. Insurance mathematics I. lecture Example – claim event At 31.12.2013 Janos fell below a tram, because of that his right leg was amputated at 01.01.2014. After that 02.11.2014 he got a resolution for 50% disability. The Society paid 500.000 HUF at 10.01.2015 to Janosne Kis.

6. Insurance mathematics I. lecture Example Insurer: Horgol Signatory: Cerna Insured: Janos Kis Beneficiary: Janosne Kis Duration: 01.01.2013 – 31.12.2013 Claim event: accidental disability of Janos Kis Sum Insured: 1.000.000 HUF Premium: 2.500 HUF Claim payment: 500.000 HUF

7. Insurance mathematics I. lecture Classification of insurance Life insurance -Traditional life - Unit-linked Nonlife insurance - Accident - Health - Liability - Casco - MTPL - Fire

8. Insurance mathematics I. lecture Other basic definitions I. Reinsurance: insurance of insurance (risk transfer, capital need decreasing) Premium elements: - net premium (due to risk) - costs - safety plus - profit rate GP=NP+C+SP+PR Written premium and earned premium

9. Insurance mathematics I. lecture Other basic definitions II. Reserves: amount which insurer has to have to cover risks and claims. Now there are a lot of kind of reserves, for example: - Mathematical reserve - Outstanding claims reserve - IBNR reserve - Unearned premium reserve, etc. In the future (during Solvency II.) there are just one (two) type(s) of reserve.

10. Insurance mathematics I. lecture Often used ratios

11. Insurance mathematics I. lecture Other basic definitions III. Risk: amount which is covered by insurance, representing with one nonnegative probability variable Number of claim: representing with one nonnegative, integer probability variable Claim: representing with one nonnegative probability variable