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Transition Matrix Theory and Loss Development John B. Mahon CARe Meeting June 6, 2005

Instrat. Transition Matrix Theory and Loss Development John B. Mahon CARe Meeting June 6, 2005. Ovewview. Transition Matrix Theory TMT Applied to GC data Distributional Model of Loss Development Independence and variation Effects on Expected Values and Increased Limits Factors. Instrat.

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Transition Matrix Theory and Loss Development John B. Mahon CARe Meeting June 6, 2005

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  1. Instrat Transition Matrix Theory and Loss DevelopmentJohn B. MahonCARe MeetingJune 6, 2005

  2. Ovewview • Transition Matrix Theory • TMT Applied to GC data • Distributional Model of Loss Development • Independence and variation • Effects on Expected Values and Increased Limits Factors

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  5. Markov Chains • Andrey Markov 1856 – 1922 • Best known for work on stochastic process theory • Markov Chains • Two essential parts • Initial distribution • Transition matrix • Need to define the array of available states • Transition matrix has two dimensions • Both are defined as the available states • Use standard matrix multiplication • Markov Property • Any information dating from before the last step for which the state of the process is known is irrelevant in predicting its state at a later step.

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  14. Data Source • Claims database of large reinsurance intermediary • DB prepared manually from submission for recovery • All values entered ground-up at 100% • Isolated claims coded GL • Eliminated claims based on loss cause description • In order to eliminate “non-standard” losses • Losses trended with Bests/Masterson’s GL BI trend

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  29. Formula for estimating mu • mu= 1.005 * ln(x), • Ingnoring the class 001 data

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  35. Function to forecast sigma values • Sigma = 1/(maturity *0.001205+ln(loss size)*0.078874-0.34447

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  41. Comparison of Transition Matrix results to Direct Transitions • Transition Matrix method assumes independence • Real Life claims are not independent • More mature transitions depend on earlier transitions • TM has no memory as to where it came from, real claims do • The TM method may introduce excessive variation

  42. Comparison of Transition Matrix results to Direct Transitions • Create initial to “final” transitions to compare with TM results • Initial is the first evaluation of a claim • “Final” is the latest evaluation of a claim • Assumed to be closed • Prepared a series of transition matrices representing various initial maturities. • Data initially as counts • Division by the initial total produces probability

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