AS462_Lec08 - ACTSC 462/862 P&C Insurance Ratemaking...

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1 ACTSC 462/862 P&C Insurance Ratemaking Lecture 8
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2 Previous Lecture >B a s i c Ratemaking – Chapter 11 Territorial boundary analysis Increased limits factors Deductibles Insurance to value/Coinsurance
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3 Basic Ratemaking Chapter 12: Credibility
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4 Basic Ratemaking – Chapter 12 > Chapter covers: • Methods for incorporating credibility in an actuarial estimate • Desirable qualities for the complement of credibility • Methods (and examples) for determining the complement of credibility in both first dollar and excess ratemaking •A brief commentary on credibility when using statistical multivariate ratemaking techniques
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5 Basic Ratemaking – Chapter 12 > Necessary Criteria: Assuming homogenous risks, the amount of credibility given to the observed experience, commonly denoted by Z , should meet the following three basic criteria: 1. Z must be greater than or equal to zero (i.e., no negative credibility) and less than or equal to 1.00 (i.e., capped at fully credible). 2. Z should increase as the number of risks underlying the actuarial estimate increases (all else being equal). 3. Z should increase at a non increasing rate.
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6 Basic Ratemaking – Chapter 12 > Classical Credibility Approach: •E s t i m a t e = Z x Observed Experience + (1.0 Z) x Related Experience First determine the expected number of claims, E(Y), required for the observed experience to be considered fully credible (Z=1.00) •T h e observed experience is considered fully credible when the probability (p) is high that the observed experience will not differ significantly from the expected experience by more than some arbitrary amount (k) Pr[(1 k)E(Y) Y (1 + k)E(Y)] = p. Partial credibility is given by the square root rule
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7 Basic Ratemaking – Chapter 12 > Classical Credibility Approach Simple example: Calculate the credibility weighted pure premium estimate assuming the following: –T h e standard for full credibility is set so that the observed value is to be within +/ 5% of the true value 90% of the time h e actuary assumes exposures are homogeneous, claim occurrence follows a Poisson distribution, and there is no variation in claim costs h e observed pure premium of $200 is based on 100 claims h e pure premium of the related experience is $300
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8 Basic Ratemaking – Chapter 12 > Classical Credibility Approach: Advantages: 1. it is the most commonly used and is therefore generally accepted 2. the data required for this approach is readily available 3. the computations are very straightforward Disadvantage: the derivation involves making several simplifying assumptions that may not be true in practice (e.g., no variation in the size of losses)
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9 Basic Ratemaking – Chapter 12 > Bühlmann Credibility: commonly referred to as least squares credibility since the goal of this approach is to minimize the square of the error between the estimate and the true expected value of the quantity being estimated –E s t i m a t e = Z x Observed Experience + (1.0 Z ) x Prior Mean •I n least squares credibility, Z is defined as follows: K N N Z + =
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10 Basic Ratemaking – Chapter 12 > Bühlmann Credibility:
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11 Basic Ratemaking – Chapter 12 > Bühlmann Credibility:
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AS462_Lec08 - ACTSC 462/862 P&C Insurance Ratemaking...

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