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Introduction

Introduction. References : Arató Miklós: Általános biztosításmatematika (General insurance mathematics ). ELTE, 2000 - Straub: Non-life Insurance Mathematics - Mikosch: Non-life Insurance Mathematics - Geiss Ch.- Geiss S.: Non-life Insurance Mathematics

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Introduction

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  1. Introduction References: Arató Miklós: Általános biztosításmatematika (General insurance mathematics). ELTE, 2000 - Straub: Non-life Insurance Mathematics - Mikosch: Non-life Insurance Mathematics - Geiss Ch.- Geiss S.: Non-life Insurance Mathematics Kaas-Goovaerts-Dhaene-Denuit: Modern Actuarial Risk Theory www.math.bme.hu\~gerenyi Requirement: Elaboration of one task from appointed home works Insurance mathematics I. lecture

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

  3. Basic question 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. Why do we take out a policy? Insurance mathematics I. lecture

  4. 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 21.12.2015. The policy contains that if Janos will be disabled in 2016 then Horgol will pay proportional part of 1 million HUF to his wife, Janosne Kis. The premium is 2.500 HUF. Insurance mathematics I. lecture

  5. Example – claim event At 31.12.2016 Janos fell below a tram, because of that his right leg was amputated at 01.01.2017. After that 02.11.2017 he got a resolution for 50% disability. The Society paid 500.000 HUF at 10.01.2018 to Janosne Kis. Insurance mathematics I. lecture

  6. Example Insurer: Horgol Signatory: Cerna Insured: Janos Kis Beneficiary: Janosne Kis Duration: 01.01.2016 – 31.12.2016 Claim event: accidental disability of Janos Kis Sum Insured: 1.000.000 HUF Premium: 2.500 HUF Claim payment: 500.000 HUF Insurance mathematics I. lecture

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

  8. 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 Other basic definitions I. Insurance mathematics I. lecture

  9. 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. Solvency II. will add other types of reserve. Other basic definitions II. Insurance mathematics I. lecture

  10. Often used ratios Insurance mathematics I. lecture

  11. 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 Other basic definitions III. Insurance mathematics I. lecture

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