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

• Homework Help
• 23

This preview shows pages 1–8. Sign up to view the full content.

BA3203 L4 BA3202 Actuarial Statistics Lecture 3 Summary: - Reinsurance

This preview has intentionally blurred sections. Sign up to view the full version.

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 2
BA3203 L4 BA3202 Actuarial Statistics Lecture 4: - Credibility theory - EBCT

This preview has intentionally blurred sections. Sign up to view the full version.

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 4
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 5 ×

This preview has intentionally blurred sections. Sign up to view the full version.

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 6 1600 2500 𝒁 ∗ 𝑿 + 𝟏 − 𝒁 𝝁 , 𝟎 ≤ 𝒁 ≤ 𝟏
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

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern