BA3202-L4 - BA3202 Actuarial Statistics Lecture 3 Summary...

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BA3203 L4 BA3202 Actuarial Statistics Lecture 3 Summary: - Reinsurance
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BA3203 L4 Reinsurance Two major forms of reinsurance Individual excess of loss Proportional reinsurance Data considerations Censored data Truncated data Actuarial Science NTU Jade Nie [email protected] 2
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BA3203 L4 BA3202 Actuarial Statistics Lecture 4: - Credibility theory - EBCT
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BA3203 L4 Objectives 1. Explain what is meant by the credibility premium formula and describe the role played by the credibility factor. 2. Explain the Bayesian approach to credibility theory and use it to derive credibility premiums in simple cases. 3. Explain the empirical Bayes approach to credibility theory, in particular its similarities with and its differences from the Bayesian approach. 4. State the assumptions underlying the two models in (3) above. 5. Calculate credibility premiums for the two models in (3). Actuarial Science NTU Jade Nie [email protected] 4
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BA3203 L4 Introduction Some basics: 𝐸 𝑋 = 𝐸 𝐸 𝑋 𝑌 𝐸 𝑓 𝑌 𝑌 = 𝑓 ( 𝑌 ) 𝐸 𝑋 𝑓 𝑌 = 𝐸 𝐸 𝑋𝑓 𝑌 𝑌 = 𝐸 𝑓 𝑌 𝐸 𝑋 𝑌 Independence: 𝐸 𝑋𝑌 = 𝐸 𝑋 𝐸 𝑌 Conditional independent: 𝐸 𝑋 1 𝑋 2 𝑌 = 𝐸 𝑋 1 𝑌 𝐸 𝑋 2 𝑌 Actuarial Science NTU Jade Nie [email protected] 5 ×
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BA3203 L4 Credibility Theory Insurers use past data from the risk itself and collateral data to estimate the expected claims in the coming year from a risk. New type of coverage Unusual risk Experience Rating Notations: 𝑋 : An estimate of the expected aggregate claims or number of claims based solely on data from the risk itself. 𝜇 : An estimate of the expected aggregate claims or number of claims based solely on collateral data. Example: Firm A wants to buy coverage for a fleet of 10 buses. Average claim of the corresponding 10 buses per year is 1,600 for the past 5 years. ( 𝑋 = 1600 ) The average claim of a fleet of busses in the entire city is 2,500. ( 𝜇 = 2500 ) Question: What is the best estimate of the expected claims for the coming year? Actuarial Science NTU Jade Nie [email protected] 6 1600 2500 𝒁 ∗ 𝑿 + 𝟏 − 𝒁 𝝁 , 𝟎 ≤ 𝒁 ≤ 𝟏
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BA3203 L4 Credibility Theory Proposed Approach: Weighted average of 𝑋 and 𝜇 𝑍 ∗ 𝑋 + 1 − 𝑍 𝜇 , 0 ≤ 𝑍 ≤ 1 How much weight should an insurer put on the average claim derived from Firm A’s fleet data ( 𝜇 )? Equivalently, how credible is the data from the risk itself, relative to the data from the larger group ( 𝑋 )? 𝑍 : the credibility factor; reflects how much “trust” is placed in the data from the risk itself ( 𝑋 ) compared with the data from the larger group ( 𝜇 ) Case 1: suppose we believe 𝑍 is 0.6 to start with 0.6 (1600) +0.4 (2500) = 1960 Case 2: the data from the risk itself is based on 10 years rather than 5 years 𝑍 should be higher than 0.6 maybe raised to 0.75 0.75 (1600) + 0.25 (2500) = 1825 Case 3: the collateral data is based on Firm B which is in a different industry
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