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AS462_Lec06

# AS462_Lec06 - ACTSC 462/862 P&C Insurance Ratemaking...

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1 ACTSC 462/862 ACTSC 462/862 P&C Insurance Ratemaking Lecture 6

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2 Previous Lecture Previous Lecture > Basic Ratemaking – Chapter 9 The importance of charging equitable rates Criteria for evaluating potential rating variables Traditional univariate (one-way) techniques used to estimate the appropriate rate differentials for various levels of a given rating variable, including distortions introduced by each
3 Basic Ratemaking Basic Ratemaking Chapter 10: Multivariate Classification

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4 Basic Ratemaking Basic Ratemaking Chapter 10 Chapter 10 > Chapter covers: • Circumstances that led to the adoption of multivariate approaches in classification ratemaking • The overall benefits of multivariate approaches • A basic explanation of the mathematical foundation of one particular multivariate method, generalized linear models (GLMs) • A sample of GLM output • Examples of statistical diagnostics associated with GLMs
5 Basic Ratemaking Basic Ratemaking Chapter 10 Chapter 10 > Shortcomings of the Univariate Methods: • they do not accurately take into account the effect of other rating variables - pure premium approach does not consider exposure correlations with other rating variables • If the rating algorithm only contained a handful of rating variables, this shortcoming could be mitigated with two-way analysis or some manual adjustments

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6 Basic Ratemaking Basic Ratemaking Chapter 10 Chapter 10 > Minimum Bias Procedures: • These are iteratively standardized univariate approaches • Each procedure involves the selection of a rating structure (e.g., additive, multiplicative or combined) and the selection of a bias function (e.g., balance principle, least squares, χ 2, and maximum likelihood bias functions). • The bias function is a means of comparing the procedure’s observed loss statistics (e.g., loss costs) to indicated loss statistics and measuring the mismatch • Both sides of this equation are weighted by the exposures in each cell to adjust for an uneven mix of business
7 Basic Ratemaking Basic Ratemaking Chapter 10 Chapter 10 > Minimum Bias Example: • Simple example assuming only two rating variables: gender (g 1 , g 2 ) and territory (t 1 , t 2 ) • The base levels, relative to which all multiplicative indications will be expressed, are female and rural (i.e. g 2 = 1.00, t 2 = 1.00) • The base rate is assumed to be \$100 Actual Loss Costs (Pure Premiums) Earned Exposures Urban Rural Total Urban Rural Total Male \$650 \$300 \$528 Male 170 90 260 Female \$250 \$240 \$244 Female 105 110 215 Total \$497 \$267 \$400 Total 275 200 475

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8 Basic Ratemaking Basic Ratemaking Chapter 10 Chapter 10 > Minimum Bias Example - Method: • set up the equations • choose initial relativities for one of the dimensions • calculate the values for the other dimension using the initial values
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AS462_Lec06 - ACTSC 462/862 P&C Insurance Ratemaking...

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