MfAD

Annotations:

• reflects the degree of uncertainty of the best actuarial estimate

1. Considerations:
   1. Knowledge
   2. Frequency and Severity
   3. Contract Duration
   4. Prob Dstr
   5. Experience
2. Reasons for fluctionation
   1. Error of estimations
   2. Insufficient or unrelaliable historical data
   3. Future conditions differ from the past
   4. Unanticipated Inluences
   5. Statistical fluctuations
3. Stochastic
   1. Key Concepts
      1. Risk Distribution
         1. probability of uncertain outcome will arrive
      2. normal distribution
         1. Why good
            1. symmetric same prob for good or bad news
            2. risk measures only with s.d, confidence level or CTE
            3. Central limit theorem

               Annotations:

               • sum of any set of homogeneous and uncorrelated risks will approximate the normal distribution as the number of risks increases to infinity
         2. Not good for insurance
            1. not enough risk
            2. individual risk are seldom sysmetric
            3. correlated with inflation, environment, court decision
      3. Standard Deviation
      4. Coefficient of variation (CV)

         Annotations:

         • s.d/mean
      5. Skewness
         1. Ins. + (many 0 claims)
         2. longer to settle, bigger skew
      6. Settlement Rate
   2. Model
      1. loss distribution using simulation
         1. assumptions, method and approximation are reasonable for the contracts
   3. Product
      1. Stop loss reinsurance
      2. Catastrophe
      3. credit, warranty, and mortgage guarantee insurance

         Annotations:

         • highly correlated with inflation, unemployment rate
      4. long tail: prof liab
         1. Extreme Event problem: low credibility data
            1. weighted average

               Annotations:

               • weighted averages of possible scenarios of relevant extreme events (usually those not reflected routinely or at all in the available data), 
            2. judgemental analysis

               Annotations:

               • of particular operational or risk issues (e.g., new claims or underwriting systems or procedures). 
   4. Quantile approcha
      1. multiple S.D
         1. simple and pracitcal
      2. percentile, VaR, Confidence level
         1. most common
         2. P(actual < mean + margin) = p
         3. depends only on the shape
            1. Improvements: add a parameter of uncertainty for the time for reflecting time (greater for long tail)
      3. CTE or Trail Value at Risk
         1. average of outcomes that exceed Qth percentile

            Annotations:

            •  a 75th percentile CTE result is the mean result of the 25% highest cost scenarios. 
            • weighted-average of the highest (100-Q)% of the results from stochastic simulation
      4. 2 insurance aspects
         1. Timing (settement pattern)
         2. Shape

            Annotations:

            •  the risk distribution of possible outcomes around the mean value, at the reporting date, over a specified time horizon
4. Deterministic
   1. Investment (i to discount)
      1. Considerations
         1. Asset/Liab matching
            1. Difficult to match asset and liability
         2. Timing
            1. Error in estimating the payment pattern
         3. Credit
            1. Asset Risk
      2. Formula
         1. Weighted formula
         2. Explicit quantification
   2. Recovery from Reinsurance
      1. Considerations
         1. Proportion
         2. Ceded LR Ceded Commission
         3. Unregistered Reins.
         4. Financial Situation
            1. Under Liquation
            2. Weak Fin. Conditions
   3. Development
      1. Considerations
         1. LOB
            1. Change in Legislation
            2. Long tail
         2. Operational
            1. Lack of Employees
            2. Lack of Guideline
            3. Employee turnover
         3. Data
            1. Credible
            2. Homogeneous
            3. Stable