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Algorithms

Algorithms. What is an algorithm? A planned sequence of calculations and decisions, basically a set of mathematical instructions How can algorithms be used? How can the Chain Ladder method be viewed as an algorithm?. Regression.

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Algorithms

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  1. Algorithms • What is an algorithm? • A planned sequence of calculations and decisions, basically a set of mathematical instructions • How can algorithms be used? • How can the Chain Ladder method be viewed as an algorithm?

  2. Regression • Mathematical technique used to estimate the parameters of a model • Simple case (line in 2 variables) Y=mX + b • Excel Functions • Function wizard

  3. Excel Regression Functions • SLOPE • INTERCEPT • STEYX • TREND • FORECAST • RSQ • LINEST

  4. Chain Ladder Method Assumptions • Linear Relationship of Incremental Losses (y=mx) • Linear relationship between incremental loss amounts and previous cumulative amount? Intercept=zero? • What does it mean if the assumption does not hold? • “Last three” selection implies a change • Does there appear to be a change? • What does this mean? • Loss development factors are uncorrelated • Do they appear correlated? • What are the implications for estimated reserves?

  5. Multiple Algorithms and Reserving • Why is reserve data organized into aggregated loss triangles? • What information is lost? • What are the advantages of using multiple algorithms? • What are the disadvantages of using multiple algorithms? • How much weight do you give to each?

  6. Lunch!

  7. Regression Models of Loss Development • Regression through the Origin Incremental Loss(y) =m*Previous Cumulative Paid Loss(x) • Regression with an intercept Incremental Loss(y) =m*Previous Cumulative Paid Loss(x) + b • Weighted Least Squares Incremental Loss(y) =m*Ultimate Loss(x) + b

  8. Model Design Considerations • Parsimony • Benefits • Pitfalls • Rank models used today • Realism • Rank models used today • How are Parsimony and Realism in conflict? • Modesty • Benefits • Robustness • Techniques for measuring • Techniques for improving

  9. Model Validation • Do the fitted values look like the actual values? • Does removing data points significantly impact the results?

  10. General Discussion

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