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Ratemaking 保险费率厘定. Steve D’Arcy 史蒂夫 · 达尔希 Chairman of the Board of the Casualty Actuarial Society 财险精算协会董事会主席 Professor of Finance at the University of Illinois 伊利诺伊大学金融学教授 Presented at Nankai University 南开大学 June 29, 2006. Overview 提纲 . Objectives in Ratemaking 保险费率厘定的目标

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ratemaking

Ratemaking 保险费率厘定

Steve D’Arcy

史蒂夫·达尔希

Chairman of the Board of the Casualty Actuarial Society

财险精算协会董事会主席

Professor of Finance at the University of Illinois

伊利诺伊大学金融学教授

Presented at Nankai University

南开大学

June 29, 2006

overview
Overview 提纲
  • Objectives in Ratemaking保险费率厘定的目标
  • Terminology术语
  • Ratemaking Methods 保险费率厘定方法
  • Advanced Issues 高级问题讨论
  • Sources for Additional Information

补充信息资源

ratemaking objectives for companies
Ratemaking Objectives for Companies公司保险费率厘定的目标

Rates should be: 费率应该:

Stable 稳定

Responsive 合理

Promote loss control 促进防损

Cover contingencies 包括意外损失

Understandable 被理解、接受

other ratemaking objectives
Other Ratemaking Objectives其它保险费率厘定目标

Regulatory view (in United States)

从法规角度看(美国)

Rates must be: 费率必须

Adequate 充足

Not excessive 不过高

Not unfairly discriminatory 不能不公平的加以区别

Financial market view从金融市场角度看

Competitive markets will assure appropriate rates

竞争的市场将会保证恰当的费率

terminology 1
Terminology – 1 术语

Exposure unit = basic rating unit 保险金额单位=基本费率单位

Example: car year

Written exposures 投保的保险金额

Exposures on policies written during period

在保险合同期内的被保金额

Earned exposures 以获保的保险金额

Exposure units actually exposed to loss during period

在保险合同期内实际已经承担损失的保险金额

Example

A policy covering 2 cars is written on October 1, 2006

一份保险单投保2辆汽车

Written exposure for 2006 = 2 car years

Earned exposure for 2006 = 2 x ¼ of a year = ½ car years

terminology 2
Terminology - 2

Written premium 保险费

Premiums booked 以入账的保险费

Earned premium 满期保险费

Pro-rata portion of premiums exposed to loss

按实际承担损失比例均摊的保险费

Claim frequency 索赔频率

Number of claims per exposure unit

每保险金额单位索赔的数量

Severity 索赔额度

Average loss per claim 每次索赔的平均赔付额

Pure premium 纯保险费

Claim frequency x severity 索赔频率乘以索赔额度

terminology 3
Terminology - 3

Loss ratio: 损失率

Incurred losses plus loss adjustment expenses

Earned premium

(发生的损失 + 损失调整费用)/ 满期保险费

Expense ratio: 费用比率 (费用 / 总保险费)

Expenses

Written premium

Surplus: 盈余

Assets – Liabilities 资产 – 负债

terminology 4
Terminology - 4

Combined ratio 联合损失率

Loss ratio + Expense ratio 损失率 + 费用比率

Underwriting profit margin (UPM) 承保利率

1 – Combined ratio 1 – 联合损失率

Operating ratio 经营比率

Combined ratio – investment income/earned premium

联合损失率 – 投资收益/满期保险费

What should be included in investment income

什么应该包括在投资收益中

Net investment income (interest, dividends and rents)

净投资收益(利息,分红和租金)

Capital gains 资本收益

Realized or unrealized 实现的或未实现的

ratemaking in the real world
Ratemaking in the Real World保险费率厘定实际应用

Incurred losses已发生的损失

Loss reserves 损失准备金

Loss development factors 损失发展因素

Inflation 通货膨胀

Other time dependent factors (auto insurance)

其它受时间影响的因素(机动车辆保险)

Traffic density 交通拥挤度

Law enforcement efforts 法律执行力度

Legal rules governing loss settlements

陪付结算的法律条例

Trending adjusts for time dependent factors

对受时间影响的因素进行趋势调整

Severity 额度

Frequency 频率

ratemaking methods
Ratemaking Methods 保险费率厘定的方法

Loss ratio method 损失率方法

Percent rate change = (A-E)/E 百分率变化

A = Actual loss ratio 实际损失率

E = Expected loss ratio 期望损失率

= 1 – Expense Ratio – Underwriting Profit Margin 1 – 费用比率 – 承保利率

Pure premium method 纯保险费方法

G = (P+F)/(1-V)

G = Gross premium 保险费总额

P = Pure premium = frequency x severity 纯保险费

F = Fixed expenses 固定费用

V = Variable expenses (and profit) 可变费用(利润)

examples
Loss Ratio Method

Actual LR = 66%

Expected LR = 60%

Percent rate change =

(66-60)/60 = +10%

Pure Premium Method

Pure premium = 400

Fixed expenses = 50

Variable expenses = 25%

Gross premium =

(400+50)/(1-.25) = 600

Examples
methods for determining the appropriate profit margin 1
Methods for Determining the Appropriate Profit Margin – 1确定恰当利润率的方法

Standard Underwriting Profit Margin 标准承保利润率

5% (or some other constant) (或其它常数)

Ignores investment income 忽略投资收益

Ignores leverage (Premium/Surplus ratio)

忽略(保险费/盈余)比率

Standard Profit Margin minus Investment Income

标准承保利润率减去投资收益

What should be included in investment income

什么应该包括在投资收益中

Net investment income (interest, dividends and rents)

净投资收益(利息,分红和租金)

Capital gains 资本收益

Realized or unrealized 实现的或未实现的

methods for determining the appropriate profit margin 2
Methods for Determining the Appropriate Profit Margin - 2

Capital Asset Pricing Model (CAPM)资本定价模型

Basic model without taxes: 不包括税收的基本模型

UPM = -k Rf + u [E(Rm) - Rf]

k = funds generating coefficient 基金产生系数

Rf = risk free rate 无风险利率

E(Rm) = Expected return on market portfolio

平均市场组合期望收益率

u = underwriting beta 保险业相对市场的beta值

No compensation for underwriting risk uncorrelated with market risk 没有考虑与市场风险不相关联的承保风险

methods for determining the appropriate profit margin 3
Methods for Determining the Appropriate Profit Margin - 3

Total Rate of Return Model 总回报率模型

TRR = (IA/S)(IR) + (P/S)(UPM)

TRR = Target total rate of return 目标回报率

IA = Investable assets 可投资资产

S = Surplus 盈余

IR = Investment return 投资回报

P = Premium 保险费

UPM = Underwriting profit margin 承保利率

How is target rate of return determined?

怎样确定目标回报率

methods for determining the appropriate profit margin 4
Methods for Determining the Appropriate Profit Margin - 4

Discounted Cash Flow Model 折现现金流模型

Equates premiums with risk adjusted cash flows for expenses, taxes and losses

经过风险调整的现金流保费收入等于支出(费用、税和损失)

Need to keep track of timing of payments

需要跟踪支付的时间

No consensus on method to determine risk adjustment

没有统一的确定风险调整的方法

Allocation and timing of surplus flows is arbitrary

盈余的分配和时间的确定是主观臆断的

general risk adjusted discount technique formula
General Risk-Adjusted Discount Technique Formula

PV (P) = PV (L) + PV (E) + PV (TUW) + PV (TII)

where:

PV = present value operator 折现指数

P = premiums 保险费

L = losses and loss adjustment expense

损失和损失调整费用

E = underwriting expenses 承保费用

TUW = taxes on underwriting profit or loss

承保利润税金

TII = taxes on investment income 投资收益税金

risk classification
Risk Classification 风险分类

For automobile insurance 机动车辆保险

Age of driver 驾驶员年龄

Sex and marital status of driver驾驶员性别和婚姻状况

Type of vehicle 车辆类型

Use of vehicle 车辆用途

Driving record of driver 驾驶员驾驶记录

Mileage driven 行驶里程

Territory where vehicle is garaged 车辆停靠地点

Other driver characteristics – use of predictive modeling

其它关于驾驶员的特征可由预测模型得到

additional sources
Additional Sources 补充的资料来源

Chapter 3 – Ratemaking by Charles McClenahan in the Foundations of Casualty Actuarial Science

Can purchase at: http://www.casact.org/pubs/castext.htm

Casualty Actuarial Society Ratemaking Seminar handouts

http://www.casact.org/coneduc/ratesem/2006/handouts/

A Comparison of Property/Casualty Insurance Financial Pricing Models by D’Arcy and Gorvett

http://www.casact.org/pubs/proceed/proceed98/980001.pdf

Ratemaking: A Financial Economics Approach by D’Arcy and Dyer

http://www.casact.org/pubs/proceed/proceed97/97301.pdf