MfAD

MfAD

1. Considerations:

   • Knowledge
   • Frequency and Severity
   • Contract Duration
   • Prob Dstr
   • Experience

2. Reasons for fluctionation

   • Error of estimations
   • Insufficient or unrelaliable historical data
   • Future conditions differ from the past
   • Unanticipated Inluences
   • Statistical fluctuations

3. Stochastic

   • Key Concepts
     • Risk Distribution
       • probability of uncertain outcome will arrive
     • normal distribution
       • Why good
         • symmetric same prob for good or bad news
         • risk measures only with s.d, confidence level or CTE
         • Central limit theorem
           • sum of any set of homogeneous and uncorrelated risks will approximate the normal distribution as the number of risks increases to infinity
       • Not good for insurance
         • not enough risk
         • individual risk are seldom sysmetric
         • correlated with inflation, environment, court decision
     • Standard Deviation
     • Coefficient of variation (CV)
       • s.d/mean
     • Skewness
       • Ins. + (many 0 claims)
       • longer to settle, bigger skew
     • Settlement Rate
   • Model
     • loss distribution using simulation
       • assumptions, method and approximation are reasonable for the contracts
   • Product
     • Stop loss reinsurance
     • Catastrophe
     • credit, warranty, and mortgage guarantee insurance
       • highly correlated with inflation, unemployment rate
     • long tail: prof liab
       • Extreme Event problem: low credibility data
         • weighted average
           • weighted averages of possible scenarios of relevant extreme events (usually those not reflected routinely or at all in the available data), 
         • judgemental analysis
           • of particular operational or risk issues (e.g., new claims or underwriting systems or procedures). 
   • Quantile approcha
     • multiple S.D
       • simple and pracitcal
     • percentile, VaR, Confidence level
       • most common
       • P(actual < mean + margin) = p
       • depends only on the shape
         • Improvements: add a parameter of uncertainty for the time for reflecting time (greater for long tail)
     • CTE or Trail Value at Risk
       • average of outcomes that exceed Qth percentile
         • &nbsp;a 75th percentile CTE result is the mean result of the 25% highest cost scenarios.&nbsp;
         • weighted-average of the highest (100-Q)% of the results from stochastic simulation
     • 2 insurance aspects
       • Timing (settement pattern)
       • Shape
         • &nbsp;the risk distribution of possible outcomes around the mean value, at the reporting date, over a specified time horizon

4. Deterministic

   • Investment (i to discount)
     • Considerations
       • Asset/Liab matching
         • Difficult to match asset and liability
       • Timing
         • Error in estimating the payment pattern
       • Credit
         • Asset Risk
     • Formula
       • Weighted formula
       • Explicit quantification
   • Recovery from Reinsurance
     • Considerations
       • Proportion
       • Ceded LR Ceded Commission
       • Unregistered Reins.
       • Financial Situation
         • Under Liquation
         • Weak Fin. Conditions
   • Development
     • Considerations
       • LOB
         • Change in Legislation
         • Long tail
       • Operational
         • Lack of Employees
         • Lack of Guideline
         • Employee turnover
       • Data
         • Credible
         • Homogeneous
         • Stable