P/C RATEMAKING AND LOSS RESERVING（PPT讲稿）CHAPTER 4 RATEMAKING

P/C RATEMAKING AND LOSS RESERVING RL Brown &L.R. gottlieb CHAPTER 4: RATEMAKING I. Introduction; Il. objectives; Data for Ratemaking; IV Premium Data V. Exposure Units; VI. The Expected Effective Period; VIl. Ingredients Vl. Rate Changes

P/C RATEMAKING AND LOSS RESERVING R.L. Brown & L.R. Gottlieb CHAPTER 4: RATEMAKING I. Introduction; II. Objectives; III. Data for Ratemaking; IV. Premium Data; V. Exposure Units; VI. The Expected Effective Period; VII. Ingredients; VIII. Rate Changes

Introduction a Objectives I. Introduction: Methods are applicable outside of PEc (e. g. health) . objectives: A. Essential objectives 1. Cover expected losses and expenses a. include investment income b. no inter-cohort subsidies c. no subsidies across risk classes d. must cover to last dollar paid out(several years later) e. selling at a loss is o. k, but subsidy should come from L.C. owners equity

2 Introduction & Objectives A. Essential Objectives 1. Cover expected losses and expenses a. include investment income b. no inter-cohort subsidies c. no subsidies across risk classes d. must cover to last dollar paid out (several years later) e. selling at a loss is O.K., but subsidy should come from I.C. owner’s equity I. Introduction: Methods are applicable outside of P&C (e.g. health) II. Objectives:

A. Essential Objectives 2. Produce rates that make adequate provision for contingencies a. The 100-year flood will happen. b. Tough to push rates up as industry is competitive and ph can often self-insure C. Inadequate rates endanger I C solvency

3 2. Produce rates that make adequate provision for contingencies a. The 100-year flood will happen! b. Tough to push rates up as industry is competitive and ph can often self-insure c. Inadequate rates endanger I.C. solvency A. Essential Objectives

A. Essential Objectives 3. Encourage loss control a. get ph to reduce claim freq severity or both b. methods used 1. good driver discounts 2. discounts for sprinklers, burg lar alarms 3. discounts for accident prevention and rehab in Wc c. leads to lower rates d. good for society

4 3. Encourage loss control a. get ph to reduce claim freq., severity or both b. methods used 1. good driver discounts 2. discounts for sprinklers, burglar alarms 3. discounts for accident prevention and rehab in W.C. c. leads to lower rates d. good for society A. Essential Objectives

A. Essential Objectives 4. Satisfy rate regulators a. rates must be adequate, not excessive and not unfairly discriminatory Too big to ignore: the impact of obesity on mortality trends Does it matter where you live? ICcB case b. some methods that are actuarially acceptable may be refused(e. g. use of age, gender and marital status as rating variables)

5 4. Satisfy rate regulators a. rates must be adequate, not excessive and not unfairly discriminatory ◼ Too big to ignore: the impact of obesity on mortality trends ◼ Does it matter where you live? ICCB Case b. some methods that are actuarially acceptable may be refused (e.g., use of age, gender and marital status as rating variables) A. Essential Objectives

B Non-Essential Objectives B Non-Essential but Desirable objectives 1. Produce rates that are reasonably stable a. rate changes must be prospectively justifiable b. reinsurance can help stability

6 B. Non-Essential but Desirable Objectives 1. Produce rates that are reasonably stable a. rate changes must be prospectively justifiable b. reinsurance can help stability B. Non-Essential Objectives

B Non-Essential Objectives 2. Produce rates that are reasonably responsive to change a. real changes(vs. one-time aberration) should be reflected(e.g. change in speed limit) b. stability and responsive are in conflict(reflecting change only to the extent it is statistically credible helps)

7 2. Produce rates that are reasonably responsive to change a. real changes (vs. one-time aberration) should be reflected (e.g. change in speed limit) b. stability and responsive are in conflict (reflecting change only to the extent it is statistically credible helps) B. Non-Essential Objectives

B Non-Essential Objectives 3. Be simple and easy to understand a. ph must understand connection to loss control to make it happen b. agents and brokers must be capable of using rate manual c. computer systems are cheaper if less complex system d. must be able to "sell " system to management and regulators(who are often not actuaries)

8 3. Be simple and easy to understand a. ph must understand connection to loss control to make it happen b. agents and brokers must be capable of using rate manual c. computer systems are cheaper if less complex system d. must be able to “sell” system to management and regulators (who are often not actuaries) B. Non-Essential Objectives

Ⅲ. Data for Ratemaking Data on claims, loss payments, and premiums may be collected and tabulated in any of the following three formats: accident year, polic year, and calendar year.(A fourth basis called the reported year, which is used for claims made policies will not be discussed here

9 III. Data for Ratemaking Data on claims, loss payments, and premiums may be collected and tabulated in any of the following three formats: accident year, policy year, and calendar year. (A fourth basis, called the reported year, which is used for claims￾made policies will not be discussed here.)

A. Accident year 1. The most common method for 中大生校內捱車撞 compiling actuarial data 2. All action of any loss 明報2008-10-25 occurring in accident year Z is held in the "accident year沙田中文大學校園内昨午1時許發生 Z”file regardless of the date of action (e. g. payment 交通意外。中大一年級女生楊慧 19歲)在大學營修樓對開橫過馬 You do not know the ultimate時,遭一輛沿大學道西行的私家 claim until the last dollar is paid 車撞倒,楊女頭部及兩腳膝部受輕 4. AlL immature data then 傷’救護員接報到場替妣包紮’楊 depend on reserve estimates 女由兩名同學陪同送院 33歲私家車司機姚ⅹ志接受酒精測 試後’證實並無飲酒’警方正調查 意外原因

10 A. Accident Year 1. The most common method for compiling actuarial data. 2. All action of any loss occurring in accident year Z is held in the “accident year Z” file regardless of the date of action (e.g. payment). 3. You do not know the ultimate claim until the last dollar is paid. 4. All immature data then depend on reserve estimates. 中大生校內捱車撞 明報 2008-10-25 沙田中文大學校園內昨午1 時許發生 交通意外。中大一年級女生楊 ×慧 （19 歲） 在大學營修樓對開橫過馬 路時，遭一輛沿大學道西行的私家 車撞倒，楊女頭部及兩腳膝部受輕 傷，救護員接報到場替她包紮，楊 女由兩名同學陪同送院…… 33 歲私家車司機姚 ×志接受酒精測 試後，證實並無飲酒，警方正調查 意外原因